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8

Original Games and Puzzles

RULES FOR COURT CIRCULAR

(A New Game of Cards for Two or More Players)

SECTION I. (For Two Players)

I

CUT for precedence. Highest is `first-hand'; lowest `dealer'. Dealer gives 6 cards to each, one by one, beginning with first-hand, and turns up the 13th, which is called the `Lead'. It is convenient that the same player should be dealer for the whole of each game.

II

First-hand then plays a card; then the other player, and so on, until 6 cards have been played, when the trick is complete, and he who can make (out of the 3 cards he has played, with or without the Lead), the best `Line', wins it.

A `Line' consists of 2, or all 3, of the cards put down by either player, with or without the Lead. In making a Line, it does not matter in what order the 3 cards have been put down. Lines rank as follows:
                        (1) 3, or 4, CARDS, (LEAD included)
Trio--i.e. 3 of a sort, (e.g. 3 Kings, or 3 Nines.)
Sequence--i.e. 3, or 4, in Sequence, (e.g. Eight, Nine, Ten, Knave.)
Sympathy--i.e. 3, or 4, Hearts.
Court--i.e. 3, or 4, Court-cards, (if 4, it is called Court Circular.)

N.B. In this Class a Line of 4 cards beats a similar Line of 3. The Lead must not be reckoned in the middle of a Sequence.

                        (2) 3 CARDS, (LEAD excluded)
Names as above.
N.B. In making a Sequence, the Ace may be reckoned either with King, Queen, or with Two, Three.
                        (3) 2 CARDS, (LEAD excluded)
Pair--i.e. 2 of a sort.
Valentine--i.e. 2 Hearts.
Etiquette--i.e. 2 Court-cards.

IV

If both have made Lines of the same kind, he whose Line contains the best card wins the trick; and if neither has made a Line, he who has played the best card wins it. Cards rank as follows:

(1) Hearts.
(2) The rest of the pack, in order Aces, Kings, &c.
N.B. If no Hearts have been played, and the highest cards on each side are equal, (e.g. if each have played an Ace), they rank in the order Diamonds, Clubs, Spades.

V

The winner of a trick chooses, as Lead for the next trick, any one of the cards on the table, except the old Lead; he then takes the rest, turning them face upwards, if he be first-hand, but if not, face downwards; and he becomes first-hand for the next trick.

VI

The dealer then gives cards to each, one by one, beginning with first-hand, until each hand is made up again to 6 cards.

VII

At any time during a trick, after the first card of it has been played, and before either has played 3 cards, he whose turn it is to play may `resign' instead; in which case no more cards are played in that trick, and the other player wins it and proceeds as in Rule V. But when either has played 3 cards, the other must not resign.

VIII

When the pack is exhausted neither player may resign. The winner of the last trick clears the board. Each then reckons up the cards he has won, which count as follows:
                              Cards face upwards                       2 each.
                                           downwards                       1
                              Hearts                                            1
                              Court-cards                                    1

(so that a Court-Heart, if face upwards, counts 4 altogether.) The winner scores the difference between his own and the loser's marks, the loser scoring nothing. Game is 20 or 50.

SECTION II. (For Three or More Players)

The same rules apply with the following necessary changes. The Lead is placed in the middle; first-hand then plays a card; then the player on his left-hand, and so on all round, each putting down his 3 cards in a row from the Lead towards himself. He who makes the best Line wins the trick, and is first-hand for the next trick. At any time during a trick, after the first card of it has been played, and before any one has played 3 cards, he whose turn it is to play may `resign' instead; in which case he loses his chance of winning that trick, and the other players go on without him. But when any one has played 3 cards, no other player may resign. In the case where all players but one `resign', he who is left to the last wins the trick. At the end of each game all the players but the lowest score the difference between their own marks and those of the lowest, the lowest scoring nothing. Game is 50.

Jan., 1860.

RULES FOR COURT CIRCULAR (ALTERNATIVE VERSION)

CUT for deal; highest is `first-hand', lowest is dealer, gives 6 cards to each, 3 at a time, turning up 13th as `Lead'. First-hand plays a card, then dealer, and so on, as numbered in the diagram, till 6 have been played, when the trick is complete. No. 5 is kept face down until No. 6 has been played.

II

Whichever has, on his side of the trick, (Lead reckoning on each side) the best `Line' of 3 cards, (`Lines' being of 3 kinds, which rank as follows: Trio, e.g. 3 Kings or 3 Nines; Sequence, e.g. Nine of Hearts, Eight of Spades, Seven of Hearts; Suit, e.g. 3 Diamonds) wins it. It does not matter in what order the cards have been played, (e.g. if `Lead' be Five of Hearts, and one of the players play Ace of Spades, Seven of Clubs, Six of Diamonds, his side contains a sequence). Trio containing `Lead' ranks above Trio not containing it, and so of Sequence and Suit. `Lead' must not be reckoned as middle card of a Sequence. An Ace will form a Sequence with Two, Three, or with King, Queen.

III

If equal Lines be made, he who has played, among the cards forming his Line, the best card (cards ranking thus: Ace of Hearts, of Diamonds, of Clubs, of Spades, King of Hearts, etc.) wins the trick; if no Line be made, he who has played the best card wins it.

IV

When the trick is won by superiority of Line, the winner adds the value of his own Line, (reckoned thus: Trio 1, Sequence 2, Suit 3,) to that of the loser's, if any, (reckoned thus: Trio 5, Sequence 3, Suit 1) and takes so many cards; when by superiority of cards, he takes one only. Lead for the next trick is then chosen from the cards left on the table, (by the winner, if both or neither have made a Line; otherwise by the loser), and the others laid aside. The loser is dealer for the next trick, and gives 3 cards to each.

V

When only 3 cards remain to be dealt, they are turned up, and each plays, either from the 3 cards in his hand, or from these 3, supplying its place from his own hand.

VI

When the pack is out, every trick (after four) counts 1; most cards, 2; most court-cards, (Aces reckoning as court-cards) 1. A Hit is 5, and two Hits make a Rubber.

April, 1862

CROQUET CASTLES

(For Five Players)

I

THIS Game requires the 10 arches, and 5 of the 8 balls used in the ordinary game, and, in addition to them, another set of 5 balls, (matching these in colour, but marked so as to be distinct from them), and 5 flags, also matching them. One set of balls is called `soldiers'; the other, `sentinels'. The arches and flags are set up as in a figure, making 5 `castles', and each player has a castle, a soldier, and a sentinel; the sentinel's `post' is half-way between the `gate' and the `door' of the castle, and the soldier is placed, to begin the game, just within the gate.

(N.B. The distance from one gate to the next should be 6 or 8 yards, and from the gate of a castle to the door 4 yards; and the distance from the door to the flag should be equal to the width of the door.)

II

The soldiers are played in order, as marked above; then the sentinels, in the same order, and so on. Each soldier has to `invade' the other 4 castles, in order, (e.g. soldier No. 3 has to invade castles Nos. 4, 5, 1, 2,) then to re-enter his own, and touch the flag; and whoever does this first, wins. To `invade' a castle, he must enter the gate, go through the door, then between the door and the flag, then out at the gate again: but he cannot enter a castle, unless either the sentinel of that castle, or his own sentinel, be out of its castle.

(N.B. No ball can enter or leave a castle, except by passing through the gate.)

III

If a sentinel touch a soldier, both being in the sentinel's castle, the soldier is `prisoner'; he is replaced (if necessary) where he was when touched, the sentinel is placed in the gate, and the castle is `fortified'. The prisoner cannot move, and nothing can go through the gate, till the castle is opened again, which is done either by the prisoner's comrade coming and touching the sentinel in the gate, or by the sentinel leaving the gate to go and rescue his own comrade: in the former case, both sentinels are replaced at their posts.

IV

When a prisoner is set free, he cannot be again taken prisoner until after his next turn.

V

If a ball touch another (except a prisoner, or a sentinel in his castle), the player may, if he likes, replace it where it was when touched, and use it to croquet his own with: in the excepted cases, he must replace it, but can do no more.

VI

If a soldier go through an arch, or between a door and flag, in his proper course, or if a sentinel go through the gate of his castle, the player has another turn.

VII

A player whose soldier is a prisoner, plays all his turns with his sentinel; and one, whose castle is fortified, with his soldier, unless it be taken prisoner, when he must play his sentinel to rescue it.

VIII

The sentinel of a fortified castle is considered to be in, or out of, the castle, as the owner chooses: that is, if he wishes to invade a castle, the sentinel of which is within it, he may consider his own sentinel as out of its castle (which gives him the right of invasion): or, if he wishes to go and rescue his soldier, he may consider it as in (so that he first plays it through the gate, and then has another turn).

Ch. Ch., Oxford, May 4, 1863.

N.B. This game does not absolutely require more than two additional balls, beside those used in the ordinary game; these may be Light Blue and Light Green, and the 10 balls may be arranged as follows--
                        Soldiers                                                             Sentinels
                        BLUE.                                                                                   LIGHT BLUE.
                        BLACK.                                                               BROWN.
                        ORANGE.                                                            YELLOW.
                        GREEN.                                                               LIGHT GREEN.
                        RED.                                                                   PINK.

MISCHMASCH

(Word-Game for Two Players or Two Sets of Players)
`Pars pro toto.'

THE essence of this game consists in one Player proposing a `nucleus' (i.e. a set of two or more letters, such as `gp', `emo', `imse'), and in the other trying to find a `lawful word' (i.e. a word known in ordinary society, and not a proper name), containing it. Thus, `magpie', `lemon', `himself', are lawful words containing the nuclei `gp', `emo', `imse'.

A nucleus must not contain a hyphen (e.g. for the nucleus `erga', `flower-garden' is not a lawful word).

Any word, that is always printed with a capital initial (e.g. `English'), counts as a proper name.

RULES

1. Each thinks of a nucleus, and says `ready' when he has done so. When both have spoken, the nuclei are named. A Player may set a nucleus without knowing of any word containing it.

2. When a Player has guessed a word containing the nucleus set to him (which need not be the word thought of by the Player who set it), or has made up his mind that there is no such word, he says `ready', or `no word', as the case may be: when he has decided to give up trying, he says `I resign'. The other must then, within a stated time (e.g. 2 minutes), say `ready', or `no word', or `I resign', or `not ready'. If he says nothing, he is assumed to be `not ready'.

3. When both have spoken, if the first speaker said `ready', he now names the word he has guessed: if he said `no word', he, who set the nucleus, names, if he can, a word containing it. The other Player then proceeds in the same way.

4. The Players then score as follows--(N.B. When a Player is said to `lose' marks, it means that the other scores them.)

Guessing a word, rightly, scores 1.
" " wrongly, loses 1.
Guessing `no word', rightly, scores 2.
" " wrongly, loses 2.
Resigning loses 1.

This ends the first move.

5. For every other move, the Players proceed as for the first move, except that when a Player is `not ready', or has guessed a word wrongly, he has not a new nucleus set to him, but goes on guessing the one in hand, having first, if necessary, set a new nucleus for the other Player.

6. A `resigned' nucleus cannot be set again during the same game. If, however, one or more letters be added or subtracted, it counts as a new one.

7. The move, in which either scores 10, is the final one; when it is completed, the game is over, and the highest score wins, or, if the scores be equal, the game is drawn.

Nov., 1882.

DOUBLETS

PREFACE

On the 29th of March, 1879, the following article appeared in Vanity Fair:--

A NEW PUZZLE

The readers of Vanity Fair have during the last ten years shown so much interest in the Acrostics and Hard Cases which were first made the object of sustained competition for prizes in this journal, that it has been sought to invent for them an entirely new kind of Puzzle, such as would interest them equally with those that have already been so successful. The subjoined letter from Mr Lewis Carroll will explain itself, and will introduce a Puzzle so entirely novel and withal so interesting, that the transmutation of the original into the final word of the Doublets may be expected to become an occupation to the full as amusing as the guessing of the Double Acrostics has already proved.

In order to enable readers to become acquainted with the new Puzzle, preliminary Doublets will be given during the next three weeks--that is to say, in the present number of Vanity Fair and in those of the 5th and 12th April. A competition will then be opened--beginning with the Doublets published on the 19th April, and including all those published subsequently, up to and including the number of the 26th July--for three prizes, consisting respectively of a Proof Album for the first and of ordinary Albums for the second and third prizes.

The rule of scoring will be as follows:--

A number of marks will be apportioned to each Doublet equal to the number of letters in the two words given. For example, in the instance given below of `Head' and `Tail', the number of possible marks to be gained would be eight; and this maximum will be gained by each one of those who make the chain with the least possible number of changes. If it be assumed that in this instance the chain cannot be completed with less than the four links given, then those who complete it with four links only will receive eight marks, while a mark will be deducted for every extra link used beyond four. Any competitor, therefore, using five links would score four, and any using twelve links or more would score nothing. The marks gained by each competitor will be published each week.

`DEAR VANITY,--Just a year ago last Christmas, two young ladies--smarting under that sorest scourge of feminine humanity, the having `nothing to do'--besought me to send them `some riddles'. But riddles I had none at hand, and therefore set myself to devise some other form of verbal torture which should serve the same purpose. The result of my meditations was a new kind of Puzzle--new at least to me--which, now that it has been fairly tested by a year's experience, and commended by many friends, I offer to you, as a newly-gathered nut, to be cracked by the omnivorous teeth which have already masticated so many of your Double Acrostics.

`The rules of the Puzzle are simple enough. Two words are proposed, of the same length: and the Puzzle consists of linking these together by interposing other words, each of which shall differ from the next word in one letter only. That is to say, one letter may be changed in one of the given words, then one letter in the word so obtained, and so on, till we arrive at the other given word. The letters must not be interchanged among themselves, but each must keep to its own place. As an example, the word `head' may be changed into `tail' by interposing the words `heal, teal, tell, tall'. I call the two given words `a Doublet', the interposed words `Links', and the entire series `a Chain', of which I here append an example:--

H E A D
h e a l
t e a l
t e l l
t a l l
T A I L

`It is, perhaps, needless to state that it is de rigueur that the links should be English words, such as might be used in good society.

`The easiest `Doublets' are those in which the consonants in one word answer to consonants in the other, and the vowels to vowels; `head' and `tail' constitute a Doublet of this kind. Where this is not the case, as in `head' and `hare', the first thing to be done is to transform one member of the Doublet into a word whose consonants and vowels shall answer to those in the other member (e.g., `head, herd, here,') after which there is seldom much difficulty in completing the `Chain'.

`I am told that there is an American game involving a similar principle. I have never seen it, and can only say of its investors, "pereant qui ante nos nostra dixerunt!'

LEWIS CARROLL.'

RULES

1. The words given to be linked together constitute a `Doublet', the interposed words are the `Links', and the entire series a `Chain'. The object is to complete the Chain with the least possible number of Links.

2. Each word in the Chain must be formed from the preceding word by changing one letter in it, and one only. The substituted letter must occupy the same place, in the word so formed, which the discarded letter occupied in the preceding word, and all the other letters must retain their places.

3. When three or more words are given to be made into a Chain, the first and last constitute a `Doublet'. The others are called `Set Links', and must be introduced into the Chain in the order in which they are given. A Chain of this kind must not contain any word twice over.

4. No word is admissible as a Link unless it (or, if it be an inflection, a word from which it comes) is to be found in the following Glossary. Comparatives and superlatives of adjectives and adverbs, when regularly formed, are regarded as `inflections' of the positive form, and are not given separately, e.g., the word `new' being given, it is to be understood that `newer' and `newest' are also admissible. But nouns formed from verbs (as `reader' from `read') are not so regarded, and may not be used as Links unless they are to be found in the Glossary.

METHOD OF SCORING, ETC.
Adopted in `Vanity Fair'

1. The marks assigned to each Doublet are as follows:--

If it be given without any Set Links, so many marks are assigned to it as there are letters in the two words together (e.g., a four-letter Doublet would have eight marks assigned to it). If it be given with Set Links, so that the Chain is made up of two or more portions, so many marks are assigned to it as would have been assigned if each portion had been a separate Chain (e.g., a four-letter Doublet which has two Set Links, so that the Chain is made up of three portions, would have twenty-four marks assigned to it).

2. Each competitor, who completes the Chain with the least possible number of Links, will receive the full number of marks assigned; and each who uses more than the least possible number of Links will lose a mark for every additional Link.

3. Each competitor is required to send his three Chains, with his signature attached, written on one piece of paper.

4. The Editor of `Vanity Fair' will be glad to receive any suggestions, both as to words which it seems desirable to omit, and as to omitted words which it seems desirable to insert; but any word proposed for insertion or for omission should be exhibited as a Link between two other words.

5. Alterations will not be made in this Glossary during any competition, but will be duly announced before the commencement of a new competition, so that those who already possess copies will be able to correct them, and will not be obliged to buy a new edition.

Vanity Fair Office

13 Tavistock Street, Covent Garden, London.

DOUBLETS ALREADY SET
In `Vanity Fair'
PRELIMINARY DOUBLETS Links
1879 Needed
March 29 Drive PIG into STY 4
Raise FOUR to FIVE 6
Make WHEAT into BREAD 6
April 5 Dip PEN into INK 5
Touch CHIN with NOSE 5
Change TEARS into SMILE 5
12 Change WET to DRY 3
Make HARE into SOUP 6
PITCH TENTS 5
FIRST COMPETITION
April 19 Cover EYE with LID 3
Prove PITY to be GOOD 6
STEAL COINS 7
April 26 Make EEL into PIE 3
Turn POOR into RICH 5
Prove RAVEN to be MISER 3
May 3 Change OAT to RYE 3
Get WOOD from TREE 7
Prove GRASS to be GREEN 7
10 Evolve MAIN from APE 5
Change CAIN into ABEL 8
Make FLOUR into BREAD 5
17 Make TEA HOT 3
Run COMB into HAIR 6
Prove a ROGUE to be a BEAST 10
24 Change ELM into OAK 7
Combine ARMY and NAVY 7
Place BEANS on SHELF 7
31 HOOK FISH 6
QUELL a BRAVO 10
Stow FURIES in BARREL 5
June 7 BUY an ASS 7
Get COAL from MINE 5
Pay COSTS in PENCE 9
14 Raise ONE to TWO 7
Change BLUE to PINK 8
Change BLACK to WHITE 6
21 Change FISH to BIRD 4
Sell SHOES for CRUST 6
Make KETTLE HOLDER 9
28 REST on SOFA 4
Trace RIVER to SHORE 10
CARESS PARENT 2
July 5 Change GRUB to MOTH 9
Turn WITCH into FAIRY 12
Make WINTER SUMMER 13
12 Save LAMB from LION 2
Crown TIGER with ROSES 5
Lay QUILT on SHEET 13
19 Put LOAF into OVEN 9
Make BREAD into TOAST 6
Put ROUGE on CHEEK 16
July 26 WHY NOT? 3
MANY will FAIL 7
to get
PRIZES from CHOKER 9

SOLUTIONS OF DOUBLETS

PRELIMINARY DOUBLETS

FIRST COMPETITION

March 29
P I G F O U R W H E A T
w  i  g f  o  u  l c  h  e  a  t
w  a  g f  o  o  l c  h  e  a  p
w  a  y f  o  o  t c  h  e  e  p
s  a  y f  o  r  t c  r  e  e  p
S T Y f  o  r  e c  r  e  e  d
f  i  r  e b  r  e  e  d
F I V E B R E A D
April 5
P E N N O S E T E A R S
e  e  n n  o  t  e s  e  a  r  s
e  e  l c  o  t  e s  t  a  r  s
e  l  l c  o  r  e s  t  a  r  e
i  l  l c  o  r  n s  t  a  l  e
i  l  k c  o  i  n s  t  i  l  e
I N K C H I N S M I L E
April 12
W E T H A R E P I T C H
b  e  t h  a  r  k p  i  n  c  h
b  e  y h  a  c  k w  i  n  c  h
d  e  y s  a  c  k w  e  n  c  h
D R Y s  o  c  k t  e  n  c  h
s  o  a  k t  e  n  t  h
s  o  a  p T E N T S
S O U P
April 19
E Y E P I T Y S T E A L
d  y  e p  i  t  s s  t  e  e  l
d  i  e p  i  n  s s  t  e  e  r
d  i  d f  i  n  s s  h  e  e  r
L I D f  i  n  d s  h  i  e  r
f  o  n  d s  h  i  e  s
f  o  o  d s  h  i  n  s
G O O D c  h  i  n  s
C O I N S
April 26
E E L P O O R R A V E N
e  e  n b  o  o  r r  i  v  e  n
p  e  n b  o  o  k r  i  s  e  n
p  i  n r  o  o  k r  i  s  e  r
P I E r  o  c  k M I S E R
r  i  c  k
R I C H
May 3
O A T T R E E G R A S S
r  a  t f  r  e  e c  r  a  s  s
r  o  t f  l  e  e c  r  e  s  s
r  o  e f  l  e  d t  r  e  s  s
R Y E f  e  e  d t  r  e  e  s
w  e  e  d f  r  e  e  s
w  e  l  d f  r  e  e  d
w  o  l  d g  r  e  e  d
W O O D G R E E N
May 10
A P E C A I N F L O U R
a  r  e c  h  i  n f  l  o  o  r
e  r  e s  h  i  n f  l  o  o  d
e  r  r s  p  i  n b  l  o  o  d
e  a  r s  p  u  n b  r  o  o  d
m  a  r s  p  u  d b  r  o  a  d
M A N s  p  e  d B R E A D
a  p  e  d
a  b  e  d
A B E L
May 17
T E A C O M B R O G U E
s  e  a c  o  m  e v  o  g  u  e
s  e  t h  o  m  e v  a  g  u  e
s  o  t h  o  l  e v  a  l  u  e
H O T h  a  l  e v  a  l  v  e
h  a  l  l h  a  l  v  e
h  a  i  l h  e  a  v  e
H A I R h  e  l  v  e
l  e  a  v  e
l  e  a  s  e
l  e  a  s  t
B E A S T
May 24
E L M A R M Y B E A N S
e  l  l a  r  m  s b  e  a  m  s
a  l  l a  i  m  s s  e  a  m  s
a  i  l d  i  m  s s  h  a  m  s
a  i  r d  a  m  s s  h  a  m  e
f  i  r d  a  m  e s  h  a  l  e
f  a  r n  a  m  e s  h  a  l  l
o  a  r n  a  v  e s  h  e  l  l
O A K N A V Y S H E L F
May 31
H O O K Q U E L L F U R I E S
h  o  o  t q  u  i  l  l b  u  r  i  e  s
h  o  s  t q  u  i  l  t b  u  r  i  e  d
h  i  s  t g  u  i  l  t b  u  r  k  e  d
f  i  s  t g  u  i  l  e b  a  r  k  e  d
F I S H g  u  i  d  e b  a  r  r  e  d
g  l  i  d  e B A R R E L
g  l  a  d  e
g  r  a  d  e
g  r  a  v  e
b  r  a  v  e
B R A V O
June 7
B U Y M I N E C O S T S
b  u  d m  i  n  t p  o  s  t  s
b  i  d m  i  s  t p  e  s  t  s
a  i  d m  o  s  t t  e  s  t  s
a  i  m m  o  a  t t  e  n  t  s
a  r  m c  o  a  t t  e  n  t  h
a  r  k C O A L t  e  n  c  h
a  s  k t  e  a  c  h
A S S p  e  a  c  h
p  e  a  c  e
P E N C E
June 14
O N E B L U E B L A C K
o  w  e g  l  u  e b  l  a  n  k
e  w  e g  l  u  t b  l  i  n  k
e  y  e g  o  u  t c  l  i  n  k
d  y  e p  o  u  t c  h  i  n  k
d  o  e p  o  r  t c  h  i  n  e
t  o  e p  a  r  t w  h  i  n  e
t  o  o p  a  n  t W H I T E
T W O p  i  n  t
P I N K
June 21
F I S H S H O E S K E T T L E
f  i  s  t s  h  o  p  s s  e  t  t  l  e
g  i  s  t c  h  o  p  s s  e  t  t  e  e
g  i  r  t c  r  o  p  s s  e  t  t  e  r
g  i  r  d c  r  o  s  s b  e  t  t  e  r
B I R D c  r  e  s  s b  e  t  t  e  d
c  r  e  s  t b  e  l  t  e  d
C R U S T b  o  l  t  e  d
b  o  l  t  e  r
b  o  l  d  e  r
H O L D E R
June 28
R E S T R I V E R C A R E S S
l  e  s  t r  o  v  e  r c  a  r  e  s  t
l  o  s  t c  o  v  e  r p  a  r  e  s  t
l  o  f  t c  o  v  e  s P A R E N T
s  o  f  t c  o  r  e  s
S O F A c  o  r  n  s
c  o  i  n  s
c  h  i  n  s
s  h  i  n  s
s  h  i  n  e
s  h  o  n  e
S H O R E
July 5
G R U B W I T C H W I N T E R
g  r  a  b w  i  n  c  h w  i  n  n  e  r
g  r  a  y w  e  n  c  h w  a  n  n  e  r
b  r  a  y t  e  n  c  h w  a  n  d  e  r
b  r  a  t t  e  n  t  h w  a  r  d  e  r
b  o  a  t t  e  n  t  s h  a  r  d  e  r
b  o  l  t t  i  n  t  s h  a  r  p  e  r
b  o  l  e t  i  l  t  s h  a  m  p  e  r
m  o  l  e t  i  l  l  s d  a  m  p  e  r
m  o  t  e f  i  l  l  s d  a  m  p  e  d
M O T H f  a  l  l  s d  a  m  m  e  d
f  a  i  l  s d  i  m  m  e  d
f  a  i  r  s d  i  m  m  e  r
F A I R Y s  i  m  m  e  r
S U M M E R
July 12
L I O N T I G E R Q U I L T
l  i  m  n t  i  l  e  r g  u  i  l  t
l  i  m  b t  i  l  e  s g  u  i  l  e
L A M B t  i  d  e  s g  u  i  d  e
r  i  d  e  s g  l  i  d  e
r  i  s  e  s s  l  i  d  e
R O S E S s  l  i  c  e
s  p  i  c  e
s  p  i  n  e
s  p  i  n  s
s  h  i  n  s
s  h  i  e  s
s  h  i  e  r
s  h  e  e  r
S H E E T
July 19
L O A F B R E A D R O U G E
l  e  a  f b  r  e  a  k r  o  u  g  h
d  e  a  f b  l  e  a  k s  o  u  g  h
d  e  a  r b  l  e  a  t s  o  u  t  h
d  e  e  r b  l  e  s  t s  o  o  t  h
d  y  e  r b  l  a  s  t b  o  o  t  h
d  y  e  s b  o  a  s  t b  o  o  t  s
e  y  e  s T O A S T b  o  a  t  s
e  v  e  s b  r  a  t  s
e  v  e  n b  r  a  s  s
O V E N c  r  a  s  s
c  r  e  s  s
c  r  e  s  t
c  h  e  s  t
c  h  e  a  t
c  h  e  a  p
c  h  e  e  p
C H E E K
July 26
W H Y M A N Y C H O K E R
w  h  o m  a  n  e c  h  o  k  e  d
w  o  o w  a  n  e c  o  o  k  e  d
w  o  t w  a  l  e l  o  o  k  e  d
N O T w  i  l  e l  o  o  s  e  d
w  i  l  l n  o  o  s  e  d
w  a  l  l n  o  i  s  e  d
w  a  i  l p  r  i  s  e  d
F A I L p  r  i  z  e  d
P R I Z E S

PREFACE TO GLOSSARY1

The following Glossary is intended to contain all well-known English words (or, if they are inflections, words from which they come) of 3, 4, 5, or 6 letters each, which may be used in good society, and which can serve as Links. It is not intended to be used as a source from which words may be obtained, but only as a test of their being admissible.

That such a Glossary is needed may best be proved by quoting the following passage from Vanity Fair of May 17, 1879, premising that all the strange words, here used, had actually occurred in Chains sent in by competitors:--

`Choker humbly presents his compliments to the four thousand three hundred and seventeen (or thereabouts) indignant Doubleteers who have so strong shent him, and pre to being soaked in the spate of their wrath, asks for a fiver of minutes for reflection. Choker is in a state of complete pye. He feels that there must be a stent to the admission of spick words. He is quite unable to sweal the chaffy spelt, to sile the porcy cole, or to swill a spate from a piny ait to the song of the spink. Frils and the mystic Gole are strangers in his sheal: the chanceful Gord hath never brought him gold, nor ever did a cate become his ain. The Doubleteers will no doubt spank him sore, with slick quotations and wild words of yore, will pour upon his head whole steres of steens and poods of spiles points downwards. But he trusts that those alone who habitually use such words as these in good society, and whose discourse is universally there understood, will be the first to cast a stean at him.'

As the chief object aimed at has been to furnish a puzzle which shall be an amusing mental occupation at all times, whether a dictionary is at hand or not, it has been sought to include in this Glossary only such words as most educated people carry in their memories. If any doubt should arise as to whether any word that suggests itself is an admissible one, it may be settled by referring to the Glossary.

When there are two words spelt alike, one a noun and one a verb, or any other such combination, it has not been thought necessary to include both, so long as all the inflections can be obtained from one: e.g. `aim' is given only as a verb, since `aims', the plural of the noun, is also the third person of the verb; but `hale, v, a,' and `hale, a,' are both given, the one being needed to supply `hales' and `haled', and the other to supply `haler'.

Two abbreviations, `e'en' and `e'er', have been included.

As to the many words which, though used and understood in good society, are yet not available as Links owing to there being no other words into which they can be changed, it has been regarded as a matter of indifference whether they are included or not.

The games of `Syzygies' and `Lanrick', invented about the same time as `Doublets', are nevertheless a good deal more complicated, and have never been so popular. The rules which follow are taken from an edition printed in 1893 for private circulation.

SYZYGIES
A WORD-PUZZLE
`Phoebus, what a name!'

1. DEFINITIONS

DEFINITION 1

When two words contain the same set of one or more consecutive letters, a copy of it, placed in a parenthesis between the two words, is called a `Syzygy', and is said to `yoke' one set to the other, and also to `yoke' each letter of one set to the corresponding letter of the other set. Examples to Def. 1
(1) (2) (3) (4)
walrus walrus walrus mine
(a) (l) (wa) (mi)
swallow swallow swallow mimic

N.B.--In Ex. (2), the Syzygy may be regarded as yoking the `l' in `walrus' to whichever `l' in `swallow' the writer may prefer. And in Ex. (4) the Syzygy may be regarded as yoking the `mi' in `mine' to whichever `mi' in `mimic' the writer may prefer.

DEFINITION 2

A set of four or more words, with a Syzygy between every two is called a `Chain', of which all but the end-words are called `Links'.

DEFINITION 3

In a `Syzygy-Problem' two words are given, which are to form the endwords of a Chain.

Example to Def. 3

If the given words are `walrus' and `carpenter' (the Problem might be stated in the form `Introduce Walrus to Carpenter'), the following Chain would be a solution of the Problem:--

WALRUS
(rus)
peruse
(per)
harper
(arpe)
CARPENTER

DEFINITION 4

Every letter in a Chain, which is not yoked to some other, is called `waste'; but, if either of the end-words contains more than 7 letters, the extra ones are not counted as waste.

Thus, in the above Chain, the `wal' in `walrus', the `e' in `peruse', the `h' in `harper', and the `c' and the `nter' in `carpenter' are `waste': so that this Chain has 10 waste letters; but since 2 of the 5 waste letters in `carpenter' are not counted as waste, the Chain is reckoned as having only 8 waste letters.

DEFINITION 5

When two words contain the same letter, but these two letters are forbidden to be yoked together, these two letters are said to be `barred' with regard to each other.

2. RULES FOR MAKING CHAINS

RULE 1

A Chain should be written as in the Example to Def. 3. It does not matter which given word is placed at the top. Any number of alternative Chains may be sent in.

RULE 2

Any word, used as a Link, must satisfy all the following tests:--

(a) It may not be foreign, unless it is in such common use that it may fairly be regarded as naturalised. (The words `ennui', `minimum', `nous', may be taken as specimens of words thus naturalised.)

(b) It must be in common use in conversation, letters, and books, in ordinary society. (Thus, slang words used only in particular localities, and words used only by specialists, are unlawful.)

(c) It may not be a proper name, when usually spelt with a capital letter. (Thus `Chinese' is unlawful; but `china', used as the name of a substance, is lawful.)

(d) It may not be an abbreviated or a compound word, when usually written with an apostrophe, or hyphen. (Thus, `silver'd', `don't', `man's', `coach-house,' are unlawful.)

N.B.--If the Scorer accepts the infinitive of a verb as `ordinary', he is bound to accept all its grammatical inflexions. Thus, if he accepts `to strop (a razor)' as an ordinary word, he is bound to accept `stroppest', `stroppeth', `stropping', and `stropped', even though the first two have probably never been used by any human being.

But, if he accepts the singular of a noun as `ordinary', he is not thereby bound to accept its plural; and vice versa.

Thus, he may accept `remorse' and `tidings' as `ordinary', and yet reject `remorses' and `tiding' as `non-ordinary'.

RULE 3

When two words begin with the same set of one or more consecutive letters, or would do so if certain prefixes were removed, each letter in the one set is `barred' with regard to the corresponding letter in the other set.

Examples to Rule 3

Certain prefixes are here marked off by perpendicular lines, and the `barred' letters are printed in italics.
(1) (2) (3) (4)
dog carriage un|done un|done
door carcase door in doors

N.B.--The letters are only `barred' as here marked. They may often be yoked in other ways: e.g., in Ex. (2), the `ca' above may be yoked to the second `ca' below.

RULE 4

When two words end with the same set of one or more consecutive letters, or would do so if certain suffixes were removed, each letter in the one set is `barred' with regard to the corresponding letter in the other set.

Examples to Rule 4

Certain suffixes are here marked off by perpendicular lines, and the `barred' letters are printed in italics.
(1) (2) (3) (4)
meat onion sink|ing sink|ing
cat moon link link|s
(5) (6)
inflat|ed plung|es
satiat|ing chang|ing

N.B.--The letters are only `barred' as here marked. They may often be yoked in other ways: e.g., in Ex. (2), the first `on' above may be yoked to the `on' below; in Ex. (3), (4), the second `in' above may be yoked to the `in' below; in Ex. (5), the `at' above may be yoked to the first `at' below; and, in Ex. (6), the `ng' above may be yoked to the second `ng' below.

Observe that, in Ex. (5), the reason why `at' is barred, is that the words become, when the suffixes are removed, `inflate' and `satiate', which end with the same 3 letters. Similarly in Ex. (6), `plunge' and `change' end with the same 3 letters. But in the words `plunges' and `singer', the `ng' is not barred, since the words `plunge' and `sing' do not end with the same letters.

RULE 5

Nouns and verbs are not to be regarded as prefixes or suffixes.

Thus `landlord (and) handmade' would be a lawful Syzygy.

RULE 6

The letters `i' and `y' may be treated as if identical. Thus `busy (usy) using' would be a lawful Syzygy.

RULE 7

The Score for a Chain may be calculated by writing down 7 numbers, as follows:--

(1) The greater No. of letters in an end-Syzygy, plus twice the least.
(2) The least No. of letters in a Syzygy.
(3) The sum of (1) plus the product of the two numbers next above (2).
(4) The No. of Links.
(5) The No. of waste letters.
(6) The sum of twice (4) plus (5).
(7) The remainder left after deducting (6) from (3). If (6) be greater than (3), the remainder is written as `o'.

No. (7) is entered as the Score of the Chain.

Example to Rule 7

The figures on the right indicate the Nos. of waste letters.

WALRUS 3
(rus)
peruse 1
(per)
harper 1
(arpe)
CARPENTER 3

As the greatest No. of letters in an end-Syzygy is `4', and the least is `3', No. (1) is `10'. Also No. (2) is `3'. Hence No. (3) is the sum of `10' plus `4 times 5', i.e., it is `30'. Also there are 2 Links and 8 waste letters. Hence No. (4) is `2', No. (5) is `8'; and No. (6) is the sum of `twice 2' plus `8'; i.e., it is `12'. Hence No. (7) is the remainder after deducting `12' from `30'; i.e., it is `18'; which is the Score for the Chain.

The result may be conveniently recorded thus:--

10, 3, 30; 2, 8, 12; 18.

The formula for the Score may, for the benefit of Algebraists, be stated thus:--

Let a = greatest No. of letters in an end-Syzygy.
b = least do.
m = least No. in a Syzygy;
l = No. of Links;
w = No. of waste letters:

then the Score = (a+2b) (m+1) (m+2) - (21+w).

3. RULES FOR SCORING CHAINS

RULE 1

If the writer of a Chain has omitted a Syzygy, the Scorer inserts a one-letter Syzygy, if he can find a lawful one.

RULE 2

If the writer has omitted a Link, the Scorer erases the two adjacent Syzygies, and proceeds as in Rule 1.

RULE 3

If a Link be mis-spelt, the Scorer corrects it.

RULE 4

If a Syzygy contains unlawful letters, the Scorer erases them, and deducts twice that number of marks from the Score.

RULE 5

If one of two consecutive Syzygies contains the other, the Scorer erases the intermediate Link, and one Syzygy containing the other.

Examples to Rule 5
(1) (2)
meeting meeting
  (ting)   (ting)
tinge tinge
  (ing)   (ting)
loving loving

N.B.--In Ex. (1) the Scorer erases `tinge' and the first Syzygy: in Ex. (2), he erases `tinge' and either Syzygy. The results are:--
(1) (2)
meeting meeting
  (ing)   (ting)
loving loving

both of which are, by Rule 4, unlawful Syzygies.

RULE 6

The penalty awarded by the preceding Rule, cannot be evaded by writing shorter Syzygies than might be claimed, so as to avoid the result of one containing the other. In such a case, the Scorer would treat them as if written in full. Examples to Rule 6

meeting
(tin)
tinge
(ng)
parting

This would be treated as if it had been written, in full.

meeting
(ting)
tinge
(ting)
parting

RULE 7

If the Chain now contains less than two Links, or an unlawful Link or Syzygy, the Scorer rejects it. Otherwise he calculates its Score.

RULE 8

In reckoning `the least number of letters in a Syzygy', the Scorer takes no notice of any Syzygies inserted by himself, unless there are no others.

RULE 9

If a writer sends in alternative Chains, the Scorer takes the best of them.

RULE 10

If all be rejected, the Scorer puts `0' against the writer's name, assigning a reason for rejecting each Chain.

RULE 11

In announcing a Problem, the Scorer may bar any word, that he likes to name, from being used as a Link. After receiving the `First-Chains', he must publish a list of the Links which he regards as violating Rule 2, and of the Syzygies which he regards as violating, owing to the occurrence of prefixes or suffixes, Rule 3 or Rule 4, and he must then allow time for sending in `Second-Chains'. He may not, when scoring, reject any `First-Chain' for a defect which ought to have been, but was not, published in the above-named list.

4. HINTS ON MAKING CHAINS

I have tried to embody some useful hints on this subject in the form of a soliloquy, supposed to be indulged in by the possessor of what Tennyson would call `a second-rate sensitive mind', while solving the problem `Turn CAMEL into DROMEDARY'.

`No use trying the whole Camel. Let's try four letters. "Came". That must be something ending in "cament", I fancy. That gives "predicament", and "medicament": I can't think of any others: and either of these would lead to "mental" or "mention". Then "amel". That gives "tamely" and "lamely". "Samely" is hardly an "ordinary" word: and I'm afraid "gamely" is slang! Well, we've got four Links, at any rate. Let's put them down:--
{predicament (ment) {mental
{(came) {medicament {mention
CAMEL {tamely
{(amel) {lamely

`NOW FOR DROMEDARY. No 5-letter Syzygy, that I can see. Let's try the 4's. "Drom". There's "loxodrome", but that's quite a specialist's word. And there's "palindrome"--no, that won't do: "palin" is a prefix. "Rome". That gives "chrome", which is not very hopeful to go on with. "Omed". That'll give us all the participles ending in "-omed": "domed", "doomed", "groomed": not very suggestive: however, there's "comedy": that sounds hopeful. "Meda". Well, there's "medal", and "medalist", and--and--that's all, I think: but "medalist" leads to "listen", or "listless". "Edar". That leads to "cedar", and words beginning with "re", such as "re-darn this stocking"--no I'm afraid that would have a hyphen! However, "cedar", leads to "dared", or any participle ending in "-ced". "Dary". There's "daring": that might lead to something such as "fringe", or "syringe". Well, let's tabulate again:--
{domed, etc.
{(omed) {comedy
{medal
{(meda) {listen
DROMEDARY {medalist (list) {listless
{(dar) dared
{(edar) cedar {(ced) . . . ced
{fringe
{(dary) daring (ring) {syringe

`Now, can we link any of these ragged ends together? "Predicament". That'll link on to "dared", though it's only a 3-letter Syzygy. That gives the Chain "Camel (came) predicament (red) dared (dar) cedar (edar) dromedary". But there's something wrong there! "Edar" contains "dar". We must write it "Camel (came) predicament (red) dared (dar) dromedary". That'll score 17. Let's try another Chain. "Predicament" and "cedar" can be linked by putting in "enticed". How will that work? "Camel (came) predicament (ent) enticed (ced) cedar (edar) dromedary". That scores only 16! Try again. "Medicament". Why that links straight on to "comedy", with a 4-letter. Syzygy! That's the best chance we've had yet. "Camel (came) medicament (medi) comedy (omed) dromedary". And what does that score, I wonder? Why it actually scores 31! Bravo!'

If any of my readers should fail, in attempting a similar soliloquy, let her say to herself, `It is not that my mind is not sensitive: it is that it is not second-rate!' Then she will feel consoled!

5. SOME Syzygy-PROBLEMS

The gentle reader (N.B. All readers are `gentle': an un-gentle reader is a lusus naturae never yet met with) may like to amuse herself by attempting (without referring to 6) some of the following Problems, solutions of which have been published in the Lady. The appended scores are the highest hitherto attained.

(1) OH DO! 11
(2) INDULGE an IDIOSYNCRASY 15
(3) Make BULLETS of LEAD 17
(4) Reconcile DOG to CAT 19
(5) COOK the DINNER 20
(6) Lay KNIFE by FORK 21
(7) CONVERSE CHEERFULLY 25
(8) SPREAD the BANQUET 27
(9) WEDNESDAY AFTERNOON 28
(10) DEMAND a CORMORANT 29

6. SOLUTIONS OF THE PROBLEMS

The appended dates refer to the numbers of the Lady in which these solutions appeared.

(1) March 24, 1892
OH 0
   (oh)
cohere 1
   (ere)
reredos 2
   (do)
DO 0

Score: -- 6, 2, 18; 2, 3, 7: 11.

(2) March 3, 1892

INDULGE 4
   (ndu)
unduly 1
   (duly)
incredulity 3
   (incr)
IDIOSYNCRASY 3

Score: -- 10,3,30; 2,11,15: 15.

(3) March 17, 1892

LEAD 1
   (lea)
plea 0
   (ple)
sample 0
   (sam)
jetsam 1
   (ets)
BULLETS 4

Score: -- 9,3,29; 3,6,12: 17.

(4) October 1, 1891

DOG 0
   (dog)
endogen 2
   (gen)
gentry 0
   (ntry)
intricate 2
   (cat)
CAT 0

Score: -- 9,3,29; 3,4,10: 19.

(5) May 5, 1892

COOK 1
   (coo)
scooping 2
   (pin)
pinned 1
   (inne)
DINNER 2

Score: -- 10,3,30; 2,6,10: 20.

(6) March 10, 1892

KNIFE 1
   (nife)
manifest 2
   (man)
workman 1
   (ork)
FORK 1

Score: -- 10,3,30; 2,5,9: 21.

(7) May 26, 1892

CONVERSE 3
   (erse)
persevering 3
   (erin)
merino 1
   (meri)
perfumery 1
   (erfu)
CHEERFULLY 3

Score: -- 12,4,42; 3,11,17: 25.

(8) May 12, 1892

SPREAD 1
   (read)
readiness 1
   (ines)
shines 0
   (shin)
vanquishing 3
   (anqu)
BANQUET 3

Score: -- 12,4,42; 3,9,15: 27.

(9) April 14, 1892

WEDNESDAY 2
   (ednes)
blessedness 3
   (esse)
finesse 1
   (iness)
craftiness 1
   (raft)
rafter 0
   (after)
AFTERNOON 2

Score: -- 15,4,45; 4,9,17: 28.

(10) March 31, 1892

DEMAND 2
   (eman)
gentleman 1
   (gent)
tangent 1
   (ange)
orange 0
   (oran)
CORMORANT 3

Score: -- 12,4,42; 3,7,13: 29.

LANRICK

A Game for Two Players

`The muster-place be Lanrick-mead.'

1. REQUISITES FOR THE GAME

This Game requires a chess or draughts board, 8 men of one colour and 8 of another (chess-pawns, draughts, or counters), and 9 pieces of card, cut to the size of a square, to serve as markers.

2. DEFINITIONS

DEFINITION 1

A `Rendezvous' is a set of squares, into which each Player tries to get his men. The position of its central square is determined by that of the Mark, and the number of its square is always one less than that of the men which are on the Board when the Mark is set. There are two kinds of Rendezvous, `close' and `open'.

DEFINITION 2

A Rendezvous must be `close', when the number of its squares is odd. It consists of the marked square and certain adjacent squares, as shown in the following diagrams, in which the Players are supposed to be at the upper and lower edges. The numerals indicate the number of Rendezvous-squares, the letter `m' the Mark, and the asterisks the Rendezvous-squares.

A 3-square Rendezvous consists of a line of 3 squares having the marked square in the middle, in any position, straight or slanting, chosen by the Player who sets the Mark.

DEFINITION 3

A Rendezvous must be `open' when the number of its squares is even. It consists of certain border-squares, which would be in `check' if the Mark were a chess-queen, as shown in the following diagrams, which are to be interpreted as in Def. 2.

For any but a 9-square Rendezvous, it will be found convenient to mark the Rendezvous-squares with pieces of card.

3. RULES

RULE 1

Each man may be moved along any line of unoccupied squares, straight or slanting, but may not (except in the case named in Rule 6) change its direction.

RULE 2

To begin the game, ten men are set as in this diagram, in which the five B's indicate black men, and the five W's white men. Then one Player sets the Mark. Both then try to play their men into the Rendezvous thus determined, he, who did not set the Mark, having the first turn.

RULE 3

In playing the first turn for a Rendezvous, a Player may move 2 squares only. In any other turn he may move 5, 4, or 3 squares, according as he has on the Board more than 4, 4, or less than 4 men. He may divide these squares among his men as he likes, but may not move more than 3 of them with any one man, unless it be his only man outside the Rendezvous. He need not move more than one square in one turn. While playing, he should count aloud the squares through or into which he moves a man. After once playing a man and letting go of it, he may not move it again in that turn.

RULE 4

The Mark, for any Rendezvous, may be set on any but a border-square; for a 3-square Rendezvous it may be set on any but a corner-square, provided that he, who sets it, has no man in the Rendezvous thus determined.

RULE 5

When the Mark has been set, he, who did not set it, may, before playing, demand an `interchange'; in which case he, who set the Mark, must interchange all his own men with whichever he chooses of the others.

RULE 6

In playing for an open Rendezvous, a Player may move any man, that is on the border, along it, without regarding the corners, as if it were one continuous line of squares; and any such man, if not moved beyond the first Rendezvous-square, reckons as having been moved one square only; but, if it be moved beyond, each square so moved must be counted as in Rule 3.

RULE 7

When a Player has got all his men into the Rendezvous, it being not yet full, he removes one of the outlying men from the Board, replacing it with a fresh man of his own colour; and this ends his turn.

RULE 8

When a Player has got all his men into the Rendezvous, it being now full, he removes the outlying man from the Board. Then he who has fewest men on the Board, or in the case of equality he who has just lost a man, sets the Mark for the next Rendezvous, as in Rule 4.

RULE 9

When a Player has only one man left, he has lost the Game.

4. HINTS TO PLAYERS

In playing for a `close' Rendezvous, remember that you have two objects in view--one to get your own men in, the other to keep the enemy's men out. A mere race for the Rendezvous is not always your best course; much may be done by getting into the way of the enemy's men, and checking their advance. Do not try to block all his men; one is generally as much as you can hope ultimately to exclude: hence it is often good play to select that man of the enemy's who is farthest from the Rendezvous and to devote to his especial benefit the services of (say) three of your own men, whose duty it will be to march, in close rank, in front of him, as a kind of `guard of honour', taking care to march in in front of him, so as to be able to announce his approach, and secure his being received with all proper respect!

It is an advantage to get hold of the central square of a `close' Rendezvous, and also of a square at that corner (or side) of it where you wish to bring in another man. As soon as the outsider has reached a square adjacent to this corner-man, he can be played in, in the following turn, by first moving the central man into some vacant Rendezvous-square, then the corner-man into the central square, and then the outsider into the corner-square.

For instance, supposing it to be a nine-square Rendezvous, and that your 5 men are A, B, C, D, E (A being in the centre), and that the enemy's 5 men are a, b, c, d, e, and that it is your turn to play; you may win the Rendezvous by moving A into the vacant square, D into A's place, and E into D's.

Similarly, in playing for an `open' Rendezvous, supposing it to consist of 8 squares (here marked by asterisks), and that your 4 men are A, B, C, D, and the enemy's 5 men a, b, c, d, e,

and that it is your turn to play; you may win the Rendezvous by moving A into the vacant Rendezvous-square, B into A's place, C into B's, and D into C's.

You should also arrange your men that are already in the Rendezvous, so as to make things comfortable for those of the enemy's men who are on their way towards it. For instance, if it be a 9-square Rendezvous, and

if there are four such men approaching from the East: by placing three of your men in the squares marked with asterisks, you may form an impenetrable wall across the Rendezvous, and thus provide a set of weary travellers--a polite attention which they will not soon forget. Similarly, if there are two of the enemy's men approaching from the North-East: by placing three of your men, as here indicated, you will provide one vacant square for

the two guests, who will probably indulge in the pathetic strain: `Now one of us must stop outside, But that one won't be me! So Tommy, make room for your Uncle!'

Should you find that the enemy is likely to get all his men into the Rendezvous, while you still have two or three men outside, remember that, as soon as all his men are in, he will replace one of your outlying men with a fresh man of his own colour; and that he will most certainly choose for this purpose whichever of the outlying men is nearest to the Rendezvous. Consequently, your best course is to have no one of them nearer than the others. Keep them all together, at the same distance from the Rendezvous, so that, whichever of them he transforms into an enemy, you can at once bar its progress with your other outlying men.

The advice I have given, as to barring the progress of the enemy's men rather than merely hurrying on with your own, is also worth remembering when playing for an `open' Rendezvous.

In carrying out the operation described in Rule 5--the interchanging of the two sets of men--difficulties may arise when men have been taken off their squares, in settling which squares they came from. These difficulties may lead to angry disputes; thence to mutual accusations of unveracity; thence to estrangement of friends; and thence to family feuds, lasting through several generations. These deplorable results may all be avoided by observing the following simple Rule:--

Move every one of the men, which are to be interchanged, into a corner of its square. Place a card-marker on a square occupied by a white man (I am supposing the two colours to be `white' and `black'), and take the white man off its square. Place this white man in the centre of a square occupied by a black man, and take the black man off its square. Place this black man in the centre of a square occupied by another white man. Proceed thus till all the men on the Board are in the centres of squares, and you have one black man in hand, which of course you place on the square indicated by the card-marker.

Rule 5 serves to prevent the Mark from being so set that he who sets it is quite certain to get his men in first--which certainly would rob the Game of much of its interest. In playing for a final 3-square Rendezvous, the mere setting of the Mark would, but for this Rule, decide the Game.

CO-OPERATIVE BACKGAMMON

Mr. Lewis Carroll . . . takes this opportunity of giving his readers the rules for Co-operative Backgammon, which he thinks will prove a novel and interesting variety of the game. (1) Each player throws three dice: with two he moves for himself, and with the third for his adversary. (2) If no one of the three dice is available for the adversary, a player may use any two he likes; otherwise he is bound to leave, as third dice, one which will be available for the adversary.

The Times: March 6, 1894.

A POSTAL PROBLEM

(June, 1891)

THE Rule, for Commissions chargeable on overdue Postal Orders, is given in the `Post Office Guide' in these words, (it is here divided, for convenience of reference, into 3 clauses)--

(a) After the expiration of 3 months from the last day of the month of issue, a Postal Order will be payable only on payment of a Commission, equal to the amount of the original poundage;

(b) with the addition (if more than 3 months have elapsed since the said expiration) of the amount of the original poundage for every further period of 3 months which has so elapsed;

(c) and for every portion of any such period of 3 months over and above every complete period.

You are requested to answer the following questions, in reference to a Postal Order for 10/-. (on which the `original poundage' would be 1d.) issued during the month of January, so that the 1st `period' would consist of the months February, March, April; the 2nd would consist of the months May, June, July; and the 3rd would consist of the months August, September, October.

(1) Supposing the Rule to consist of clause (a) only, on what day would a `Commission' begin to be chargeable? ( )

(2) What would be its amount? ( )

(3) Supposing the Rule to consist of clauses (a) and (b), on what day would the lowest `Commission' begin to be chargeable? ( )

(4) What would be its amount? ( )

(5) On what day would a larger `Commission' (being the sum of 2 `Commissions') begin to be chargeable? ( )

(6) What would be its amount? ( )

(7) On what day would a yet larger `Commission' begin to be chargeable? ( )

(8) What would be its amount? ( )

(9) Taking the Rule as consisting of all 3 clauses, in which of the above-named 3 `periods' does clause (c) first begin to take effect? ( )

(10) Which day, of any `period', is the earliest on which it can be said that a `portion' of the `period' has elapsed? ( )

(11) On what day would the lowest `Commission' begin to be chargeable? ( )

(12) What would be its amount? ( )

(13) On what day would a larger `Commission' begin to be chargeable? ( )

(14) What would be its amount? ( )

(15) On what day would a yet larger `Commission' begin to be chargeable? ( )

(16) What would be its amount? ( )

Signature . . . . .
Date . . . . .

SUPPLEMENT

THE Rule is given, below, in a form which exhibits its grammatical construction--

                 (a. 1) After the expiration of 3 months
                    from the last day of the month of
                      issue, a Postal Order will be
                        payable only on payment
				  |
		   --------------------------------
                                                  |
                                         (b.1) with the addition (if more
                                         than 3 months have elapsed since 
              of                                 the said expiration)
(a.2) a Commission, equal to the                        of
amount of the original poundage             the amount of the original
                                                     poundage
		   --------------------------------
                                                  |
             for                               and for
     (b.2) every further period         (c.) every portion of any
     of 3 months which has so           such period of 3 months
             elapsed                     over and above every
                                           complete period.

WHAT THE TORTOISE SAID TO ACHILLES

ACHILLES had overtaken the Tortoise, and had seated himself comfortably on its back.

`So you've got to the end of our race-course?' said the Tortoise. `Even though it does consist of an infinite series of distances? I thought some wiseacre or other had proved that the thing couldn't be done?'

`It can be done,' said Achilles. `It has been done! Solvitur ambulando. You see the distances were constantly diminishing: and so--'

`But if they had been constantly increasing?' the Tortoise interrupted. `How then?'

`Then I shouldn't be here,' Achilles modestly replied; `and you would have got several times round the world, by this time!'

`You flatter me--flatten, I mean,' said the Tortoise; `for you are a heavy weight, and no mistake! Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one?'

`Very much indeed!' said the Grecian warrior, as he drew from his helmet (few Grecian warriors possessed pockets in those days) an enormous note-book and a pencil. `Proceed! And speak slowly, please! Short-hand isn't invented yet!'

`That beautiful First Proposition of Euclid!' the Tortoise murmured dreamily. `You admire Euclid?'

`Passionately! So far, at least, as one can admire a treatise that wo'n't be published for some centuries to come!'

`Well, now, let's take a little bit of the argument in that First Proposition--just two steps, and the conclusion drawn from them. Kindly enter them in your note-book. And in order to refer to them conveniently, let's call them A, B, and Z:

(A) Things that are equal to the same are equal to each other.
(B) The two sides of this Triangle are things that are equal to the same.
(Z) The two sides of this Triangle are equal to each other.

`Readers of Euclid will grant, I suppose, that Z follows logically from A and B, so that any one who accepts A and B as true, must accept Z as true?'

`Undoubtedly! The youngest child in a High School--as soon as High Schools are invented, which will not be till some two thousand years later--will grant that.'

`And if some reader had not yet accepted A and B as true, he might still accept the Sequence as a valid one, I suppose?'

`No doubt such a reader might exist. He might say "I accept as true the Hypothetical Proposition that, if A and B be true, Z must be true; but I don't accept A and B as true." Such a reader would do wisely in abandoning Euclid, and talking to football.'

`And might there not also be some reader who would say "I accept A and B as true, but I don't accept the Hypothetical"?'

`Certainly there might. He, also, had better take to football.'

`And neither of these readers,' the Tortoise continued, `is as yet under any logical necessity to accept Z as true?'

`Quite so,' Achilles assented.

`Well, now, I want you to consider me as a reader of the second kind, and to force me, logically, to accept Z as true.'

`A tortoise playing football would be--' Achilles was beginning.

`--an anomaly, of course,' the Tortoise hastily interrupted. `Don't wander from the point. Let's have Z first, and football afterwards!'

`I'm to force you to accept Z, am I?' Achilles said musingly. `And your present position is that you accept A and B, but you don't accept the Hypothetical--'

`Let's call it C,' said the Tortoise.

`--but you don't accept:

(C) If A and B are true, Z must be true.'

`That is my present position,' said the Tortoise.

`Then I must ask you to accept C.'

`I'll do so,' said the Tortoise, `as soon as you've entered it in that note-book of yours. What else have you got in it?'

`Only a few memoranda,' said Achilles, nervously fluttering the leaves: `a few memoranda of--of the battles in which I have distinguished myself!'

`Plenty of blank leaves, I see!' the Tortoise cheerily remarked. `We shall need them all!' (Achilles shuddered.) `Now write as I dictate:

(A) Things that are equal to the same are equal to each other.

(B) The two sides of this triangle are things that are equal to the same.

(C) If A and B are true, Z must be true.

(Z) The two sides of this Triangle are equal to each other.'

`You should call it D, not Z,' said Achilles. `It comes next to the other three. If you accept A and B and C, you must accept Z.'

`And why must I?'

`Because it follows logically from them. If A and B and C are true, Z must be true. You don't dispute that, I imagine?'

`If A and B and C are true, Z must be true,' the Tortoise thoughtfully repeated. `That's another Hypothetical, isn't it? And, if I failed to see its truth, I might accept A and B and C, and still not accept Z, mightn't I?'

`You might,' the candid hero admitted; `though such obtuseness would certainly be phenomenal. Still, the event is possible. So I must ask you to grant one more Hypothetical.'

`Very good. I'm quite willing to grant it, as soon as you've written it down. We will call it

(D) If A and B and C are true, Z must be true.

`Have you entered that in your note-book?'

`I have!' Achilles joyfully exclaimed, as he ran the pencil into its sheath. `And at last we've got to the end of this ideal race-course! Now that you accept A and B and C and D, of course you accept Z.'

`Do I?' said the Tortoise innocently. `Let's make that quite clear. I accept A and B and C and D. Suppose I still refuse to accept Z?'

`Then Logic would take you by the throat, and force you to do it!' Achilles triumphantly replied. `Logic would tell you "You ca'n't help yourself. Now that you've accepted A and B and C and D, you must accept Z!" So you've no choice, you see.'

`Whatever Logic is good enough to tell me is worth writing down,' said the Tortoise. `So enter it in your book, please. We will call it

(E) If A and B and C and D are true, Z must be true.

`Until I've granted that, of course, I needn't grant Z. So it's quite a necessary step, you see?'

`I see,' said Achilles; and there was a touch of sadness in his tone.

Here the narrator, having pressing business at the Bank, was obliged to leave the happy pair, and did not again pass the spot until some months afterwards. When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his note-book, which appeared to be nearly full. The Tortoise was saying `Have you got that last step written down? Unless I've lost count, that makes a thousand and one. There are several millions more to come. And would you mind, as a personal favour--considering what a lot of instruction this colloquy of ours will provide for the Logicians of the Nineteenth Century--would you mind adopting a pun that my cousin the Mock-Turtle will then make, and allowing yourself to be re-named Taught-Us?'

`As you please!' replied the weary warrior, in the hollow tones of despair, as he buried his face in his hands. `Provided that you, for your part, will adopt a pun the Mock-Turtle never made, and allow yourself to be renamed A Kill-Ease!'

A LOGICAL PARADOX

`WHAT, nothing to do?' said Uncle Jim. `Then come along with me down to Allen's. And you can just take a turn while I get myself shaved.'

`All right,' said Uncle Joe. `And the Cub had better come too, I suppose?'

The `Cub' was me, as the reader will perhaps have guessed for himself. I'm turned fifteen--more than three months ago; but there's no sort of use in mentioning that to Uncle Joe; he'd only say, `Go to your cubbicle, little boy!' or, `Then I suppose you can do cubbic equations?' or some equally vile pun. He asked me yesterday to give him an instance of a Proposition in A. And I said, `All uncles make vile puns.' And I don't think he liked it. However, that's neither here nor there. I was glad enough to go. I do love hearing those uncles of mine `chop logic', as they call it; and they're desperate hands at it, I can tell you!

`That is not a logical inference from my remark,' said Uncle Jim.

`Never said it was,' said Uncle Joe; `it's a Reductio ad Absurdum.'

`An Illicit Process of the Minor!' chuckled Uncle Jim.

That's the sort of way they always go on, whenever I'm with them. As if there was any fun in calling me a Minor!

After a bit, Uncle Jim began again, just as we came in sight of the barber's. `I only hope Carr will be at home,' he said. `Brown's so clumsy. And Allen's hand has been shaky ever since he had that fever.'

`Carr's certain to be in,' said Uncle Joe.

`I'll bet you sixpence he isn't!' said I.

`Keep your bets for your betters,' said Uncle Joe. `I mean'--he hurried on, seeing by the grin on my face what a slip he'd made--`I mean that I can prove it, logically. It isn't a matter of chance.'

`Prove it logically!' sneered Uncle Jim. `Fire away, then! I defy you to do it!'

`For the sake of argument,' Uncle Joe began, `let us assume Carr to be out. And let us see what that assumption would lead to. I'm going to do this by Reductio ad Absurdum.

`Of course you are!' growled Uncle Jim. `Never knew any argument of yours that didn't end in some absurdity or other!'

`Unprovoked by your unmanly taunts,' said Uncle Joe in a lofty tone, `I proceed. Carr being out, you will grant that, if Allen is also out, Brown must be at home?'

`What's the good of his being at home?' said Uncle Jim. `I don't want Brown to shave me! He's too clumsy.'

`Patience is one of those inestimable qualities--' Uncle Joe was beginning; but Uncle Jim cut him off short.

`Argue!' he said. `Don't moralise!'

`Well, but do you grant it?' Uncle Joe persisted. `Do you grant me that, if Carr is out, it follows that if Allen is out Brown must be in?'

`Of course he must,' said Uncle Jim; `or there'd be nobody to mind the shop.'

`We see, then, that the absence of Carr brings into play a certain Hypothetical, whose protasis is "Allen is out", and whose apodosis is "Brown is in". And we see that, so long as Carr remains out, this Hypothetical remains in force?'

`Well, suppose it does. What then?' said Uncle Jim.

`You will also grant me that the truth of a Hypothetical--I mean its validity as a logical sequence--does not in the least depend on its protasis being actually true, nor even on its being possible. The Hypothetical "If you were to run from here to London in five minutes you would surprise people", remains true as a sequence, whether you can do it or not.'

`I can't do it,' said Uncle Jim.

`We have now to consider another Hypothetical. What was that you told me yesterday about Allen?'

`I told you,' said Uncle Jim, `that ever since he had that fever he's been so nervous about going out alone, he always takes Brown with him.'

`Just so,' said Uncle Joe. `Then the Hypothetical "If Allen is out Brown is out" is always in force, isn't it?"

`I suppose so,' said Uncle Jim. (He seemed to be getting a little nervous himself now.)

`Then, if Carr is out, we have two Hypotheticals, "if Allen is out Brown is in", 'and "if Allen is out Brown is out", in force at once. And two incompatible Hypotheticals, mark you! They can't possibly be true together!'

`Can't they?' said Uncle Jim.

`How can they?' said Uncle Joe. `How can one and the same protasis prove two contradictory apodoses? You grant that the two apodoses, "Brown is in" and "Brown is out", are contradictory, I suppose?'

`Yes, I grant that,' said Uncle Jim.

`Then I may sum up,' said Uncle Joe. `If Carr is out, these two Hypotheticals are true together. And we know that they cannot be true together. Which is absurd. Therefore Carr cannot be out. There's a nice Reductio ad Absurdum for you!'

Uncle Jim looked thoroughly puzzled; but after a bit he plucked up courage, and began again. `I don't feel at all clear about that incompatibility. Why shouldn't those two Hypotheticals be true together? It seems to me that would simply prove "Allen is in". Of course, it's clear that the apodoses of those two Hypotheticals are incompatible--"Brown is in" and "Brown is out". But why shouldn't we put it like this? If Allen is out Brown is out. If Carr and Allen are both out, Brown is in. Which is absurd. Therefore Carr and Allen can't be both of them out. But, so long as Allen is in, I don't see what's to hinder Carr from going out.'

`My dear, but most illogical brother!' said Uncle Joe. (Whenever Uncle Joe begins to "dear" you, you may make pretty sure he's got you in a cleft stick!) `Don't you see that you are wrongly dividing the protasis and the apodosis of that Hypothetical? Its protasis is simply "Carr is out"; and its apodosis is a sort of sub-Hypothetical, "If Allen is out, Brown is in". And a most absurd apodosis it is, being hopelessly incompatible with that other Hypothetical, that we know is always true, "If Allen is out, Brown is out". And it's simply the assumption "Carr is out" that has caused this absurdity. So there's only one possible conclusion--Carr is in!'

A HEMISPHERICAL PROBLEM

HALF of the world, or nearly so, is always in the light of the sun: as the world turns round, this hemisphere of light shifts round too, and passes over each part of it in succession.

Supposing on Tuesday, it is morning at London; in another hour it would be Tuesday morning at the west of England; if the whole world were land we might go on tracing1 Tuesday morning, Tuesday morning all the way round, till in twenty-four hours we get to London again. But we know that at London twenty-four hours after Tuesday morning it is Wednesday morning. Where, then, in its passage round the earth, does the day change its name? Where does it lose its identity?

Practically there is no difficulty in it, because a great part of the journey is over water, and what it does out at sea no one can tell: and besides there are so many different languages that it would be hopeless to attempt to trace the name of any one day all the year round. But is the case inconceivable that the same land and the same language should continue all round the world? I cannot see that it is: in that case either1 there would be no distinction at all between each successive day, and so week, month, etc., so that we should have to say, `The Battle of Waterloo happened to-day, about two million hours ago', or some line would have to be fixed where the change should take place, so that the inhabitants of one house would wake and say, `Heigh-ho,2 Tuesday morning!' and the inhabitants of the next (over the line), a few miles to the west would wake a few minutes afterwards and say, `Heigh-ho! Wednesday morning!' What hopeless confusion the people who happened to live on the line would be in, is not for me to say. There would be a quarrel every morning as to what the name of the day should be. I can imagine no third case, unless everybody was allowed to choose for themselves, which state of things would be rather worse than either of the other two.

I am aware that this idea has been started before -- namely, by the unknown author of that beautiful poem beginning, `If all the world were apple pie,' etc.3 The particular result here discussed, however, does not appear to have occurred to him as he confines himself to the difficulties in obtaining drink which would certainly ensue.

WHERE DOES THE DAY BEGIN?

OBSERVING that this question is now under discussion in your columns (a question which occurred to myself years ago, and for which I have never been able to meet with a satisfactory solution), I am anxious that your correspondents should be aware what the real difficulty is. According to the statement of `T.J. Buckton, Lichfield', the day is always commencing at some point or other on the globe; so that if one could travel round it in twenty-four hours, arriving everywhere exactly at midnight by the time of the place, we should find each place in a transition of name. But if for midnight we substitute midday we are at once involved in a difficulty: the case may be briefly stated thus: -- Suppose yourself to start from London at midday on Tuesday, and to travel with the sun, thus reaching London again at midday on Wednesday. If at the end of every hour you ask the English residents in the place you have reached the name of the day, you must at last reach some place where the answer changes to Wednesday. But at that moment it is still Tuesday (1 p.m.) at the place you left an hour before. Thus you find two places within an hour in time of each other using different names for the same day, and that not at midnight when it would be natural to do so, but when one place is at midday and the other at 1 p.m. Whether two such places exist, and whether, if they do exist, any communication can take place between them without utter confusion being the result, I shall not pretend to say: but I shall be glad to see any rational solution suggested for the difficulty as I have put it.

The Illustrated London News
April 18, 1857

THE TWO CLOCKS

WHICH is better, a clock that is right only once a year, or a clock that is right twice every day? `The latter,' you reply, `unquestionably.' Very good, now attend.

I have two clocks: one doesn't go at all, and the other loses a minute a day: which would you prefer? `The losing one,' you answer, `without a doubt.' Now observe: the one which loses a minute a day has to lose twelve hours, or seven hundred and twenty minutes before it is right again, consequently it is only right once in two years, whereas the other is evidently right as often as the time it points to comes round, which happens twice a day.

So you've contradicted yourself once.

`Ah, but,' you say, `what's the use of its being right twice a day, if I ca'n't tell when the time comes?'

Why, suppose the clock points to eight o'clock, don't you see that the clock is right at eight o'clock? Consequently, when eight o'clock comes round your clock is right.

`Yes, I see that,' you reply.

Very good, then you've contradicted yourself twice: now get out of the difficulty as best you can, and don't contradict yourself again if you can help it.

You might go on to ask, `How am I to know when eight o'clock does come? My clock will not tell me.' Be patient: you know that when eight o'clock comes your clock is right, very good; then your rule is this: keep your eye fixed on your clock, and the very moment it is right it will be eight o'clock. `But----,' you say. There, that'll do; the more you argue the farther you get from the point, so it will be as well to stop.

PROBLEMS AND CURIOSITIES

The following diagram, which should be copied upon a square piece of paper,

and then cut out along the dotted lines, represents another favourite puzzle of Mr. Dodgson's. When the square has been divided into its four sections it will be found that they may not only be arranged as a square but also as an oblong. In the first case the figure appears to be made up of sixty-four small squares, in the second of sixty-five, and the puzzle is to account for this discrepancy.

1

Four gentlemen and their wives wanted to cross the river in a boat that would not hold more than two at a time.

The conditions were, that no gentleman must leave his wife on the bank unless with only women or by herself, and also that some one must always bring the boat back.

How did they do it?

2

A customer bought goods in a shop to the amount of 7/3d. The only money he had was a half-sovereign, a florin and a sixpence: so he wanted change. The shopman only had a crown, a shilling, and a penny. But a friend happened to come in, who had a double-florin, a half-crown, a fourpenny-bit, and a threepenny-bit.

Could they manage it?

3

A captive Queen and her son and daughter were shut up in the top room of a very high tower. Outside their window was a pulley with a rope round it, and a basket fastened at each end of the rope of equal weight. They managed to escape with the help of this and a weight they found in the room quite safely. It would have been dangerous for any of them to come down if they weighed more than 15 lb. more than the contents of the lower basket, for they would do so too quickly, and they also managed not to weigh less either.

The one basket coming down would naturally of course draw the other up.

How did they do it?

The Queen weighed 195 lb., daughter 165, son 90, and the weight 75.

This is an addition to the puzzle --

The Queen had with her in the room, besides her son and daughter and the weight, a pig weighing 60 lb., a dog 45 lb., and a cat 30. These have to be brought down safely too, with the same restriction. The weight can come down any way, of course.

The additional puzzle consists in this -- there must be some one at each end to put the animals into and out of the baskets.

4

Put down any number of pounds not more than twelve, any number of shillings under twenty, and any number of pence under twelve. Under the pounds put the number of pence, under the shillings the number of shillings, and under the pence the number of pounds, thus reversing the line.

Subtract.
Reverse the line again.
Add.

Answer, £12 18s. 11d., whatever numbers may have been selected.

5
A MAGIC NUMBER
142857
285714 twice that number.
428571 thrice that number.
571428 four times that number.
714285 five times that number.
857142 six times that number.

Begin at the `1' in each line and it will be the same order of figures as the magic number up to six times that number, while seven times the magic number results in a row of 9's.

LAWN TENNIS TOURNAMENTS

The True Method of Assigning Prizes with a Proof of the Fallacy of the Present Method

1. Introductory

AT a Lawn Tennis Tournament, where I chanced, some while ago, to be a spectator, the present method of assigning prizes was brought to my notice by the lamentations of one of the Players, who had been beaten (and had thus lost all chance of a prize) early in the contest, and who had had the mortification of seeing the 2nd prize carried off by a Player whom he knew to be quite inferior to himself. The results of the investigations, which I was led to make, I propose to lay before the reader under the following four headings --

(a) A proof that the present method of assigning prizes is, except in the case of the first prize, entirely unmeaning.

(b) A proof that the present method of scoring in matches is constantly liable to lead to unjust results.

(c) A system of rules for conducting Tournaments, which, while requiring even less time than the present system, shall secure equitable results.

(d) An equitable system for scoring in matches.

2. A proof that the present method of assigning prizes is, except in the case of the first prize, entirely unmeaning.

Let us take, as an example of the present method, a Tournament of 32 competitors with 4 prizes.

On the 1st day, these contend in 16 pairs: on the 2nd day, the 16 Winners contend in 8 pairs, the Losers being excluded from further competition: on the 3rd day, the 8 Winners contend in 4 pairs: on the 4th day, the 4 Winners (who are now known to be the 4 Prize-Men) contend in 2 pairs; and on the 5th day, the 2 Winners contend together to decide which is to take the 1st prize and which the 2nd -- the two Losers having no further contest, as the 3rd and 4th prizes are of equal value.

Now, if we divide the list of competitors, arranged in the order in which they are paired, into 4 sections, we may see that all that this method really does is to ascertain who is best in each section, then who is best in each half of the list, and then who is best of all. The best of all (and this is the only equitable result arrived at) wins the 1st prize: the best in the other half of the list wins the 2nd: and the best men in the two sections not yet represented by a champion win the other two prizes. If the Players had chanced to be paired in the order of merit, the 17th best Player would necessarily carry off the 2nd prize, and the 9th and 25th best the 3rd and 4th! This of course is an extreme case: but anything within these limits is possible: e.g. any competitor, from the 3rd best to the 17th best, may, by the mere accidental arrangement of pairs, and by no means as a result of his own skill, carry off the 2nd prize. As a mathematical fact, the chance that the 2nd best Player will get the prize he deserves is only 16/31sts; while the chance that the best 4 shall get their proper prizes is so small, that the odds are 12 to 1 against its happening!

If any one thinks that, after all, we are merely introducing another element of chance into the game, and that no one can fairly object to that, let him try the experiment in a rifle competition. Let him interpose when the man, who has made the 2nd best score, is going to receive his prize, and propose that he shall draw a counter from a bag containing 16 white and 15 black, and only have his prize in case he draw a white one: and let him observe the expression of that rifleman's face.

3. A proof that the present method of scoring in matches is constantly liable to lead to unjust results.

To prove this, let us suppose a `set' to mean `the best of 11 games' and a `match' `the best of 5 sets': i.e. `he, who first wins 6 games, wins a set; he, who first wins 3 sets, wins a match.'

Suppose A and B to play the following 50 games (`A2' means A wins 2 games, and so on) --

B2A5B4|A6|B3A5B2A*|B*A2B4A3B|B2A5B34.

Here A wins 28 games to 22, and also wins the match.

But, by simply transposing A*, B*, we get

B2A5B4|A6|B3A5B3|A3B4A3|B3A5B3, the last game of the original series not being played.

Here A still wins 27 games to 22: yet he loses the match!

4. A system of rules for conducting Tournaments, which while requiring even less time than the present system, shall secure equitable results.

The method for conducting Tournaments, which I have to propose, involves two departures from the present method. First, I propose to make a `match' last only half a day (the necessary reduction in the number of games I will discuss in section 5): secondly, I propose to give only 3 prizes. The rules for a Tournament of 32 Players would be as follows --

(a) The Tournament begins in the middle of the 1st day, so that there is only one contest that day -- the 32 Players being arranged in 16 pairs.

(b) A list is kept, and against each name is entered, at the end of each contest, the name of any one who has been superior to him -- whether by actually beating him, or by beating some one who has done so (thus, if A beats B, and B beats C, A and B are both `superiors' of C). So soon as any name has 3 `superiors' entered against it, it is struck out of the list.

(c) For the 2nd day (morning) the 16 unbeaten men are paired together, and similarly the 16 with 1 superior (the Losers in these last-named pairs will now have 3 superiors each, and will therefore be struck off the list). In all other contests they are paired in the same way: first pairing the unbeaten, then those with 1 superior, and so on, and avoiding, as far as possible, pairing two Players who have a common superior.

(d) By the middle of the 3rd day the unbeaten are reduced to two, one of whom is certainly `First-prize-man'. These two do not contend in the afternoon contest that day, but have a whole-day match on the 4th day -- the other Players meanwhile continuing the usual half-day matches.

(e) By the end of the 4th day, the `First-prize-man' is known (by the very same process of elimination used in the existing method): and the remaining Players are paired by the same rules as before, for the 2 contests on the 5th day. If, in section (a), the Tournament was begun in the morning, the two men named in section (d) being still allowed a whole-day match, nothing would be gained in time, as the Tournament would take 4½ days, while much would be lost in interest, as the first prize would be settled in 3 days.

To illustrate these rules, I will give the complete history of a Tournament of 32 competitors, with 3 prizes. If the reader will draw out the following Tables, in blank, and fill them up for himself, referring, if necessary, to the accompanying directions, he will easily understand the workings of system.

Let the Players be arranged alphabetically, and let the relative skill with which they play in this Tournament, be --
A B C D E F G H J
19 22 14 32 16 25 15 28 3
K L M N P Q R S T
10 8 1 29 4 12 2 17 23
U V W X Y Z a b c
26 11 20 31 13 18 6 24 9
d e f g h
21 30 5 7 27

These numbers (`1' meaning `best') will enable the reader to name the victor in any contest: but of course they are not supposed to be known to the Tournament-Committee, who have nothing to guide them but the results of actual contests. In the following Tables, `I(e)' means `first day, evening', and so on: also a Player, who is virtually proved superior to another, is entered thus `(A)'. The victor in each contest is marked*: and means `struck out'.

Directions for filling in the Tables --

Tab. I Day I (e). The names are written out alphabetically, and paired as they stand. The victors are marked with asterisks.

Tab. II. Day I (e). As B has been beaten by A, A is entered as his `superior'; C as D's superior; and so on.

Tab. I. Day II (m). We first pair together all the unbeaten, A,C,E,G, &c. Then those who have one superior, B,D,F,H, &c.

Tab. II. Day II (m). We first enter the actual superiors, C,G, &c. Then, since A has a superior C, and B has a superior A, we see that B has a virtual superior C; and so on. We then see that D has 3 superiors, and must be struck out; and so with H, &c.

Tab. I. Day II (e). We first pair together all the unbeaten, C,G, &c. Then all with one superior, A,E, &c.; but when we come to J,L, we find we have a common superior; so we pair J with P, and L with Q. This series ends with an odd one, g, who must therefore be paired with the first of those who have two superiors each, F,T, &c.

Tab. I. Day III (m). Here, in pairing those with one superior, we again end with an odd one, g, who must therefore be paired with the first of those with two superiors, viz. T. We end with an `odd man', c.

Tab. II. Day III (m). The unbeaten are now reduced to one pair, M, f, who therefore will do nothing this afternoon, but will have a whole-day contest to-morrow.

Tab. I. Day III (e). Those who have one superior are C,J,L,R, all with a common superior M; and then V,a,g, all with a common superior f. We therefore pair C with V, and so on, leaving an odd one R, who must be paired with the only one who has two superiors, viz. c.

Tab. II. Day III (e). Enter as usual.

Tab. I. Day IV (m). We pair the 2 unbeaten, M,f, for their whole-day contest. Then those with one superior.

Tab. II. Day IV (m). M and f are still contending. V and g are struck out.

Tab. I Day IV (e). J and R must be paired together, though they have a common superior.

Tab. I. Day IV (e). M is First-prize-man.

Tab. I. Day V (m). R and f must be paired together, though they have a common superior. J is `odd man'.

Tab. II. Day V (m). R is now the only man with one superior, and is therefore Second-prize-man.

Tab. I. Day V (e). J and f contend for the Third prize.

If this Tournament were fought by the present method, the 4 Prize men would be C,M,V,f: f would get the 2nd prize, and C and V the 3rd and 4th: i.e. the 5th best man would get the 2nd prize, and the 14th and 11th best the other two.

5. An equitable system for scoring in matches.

In order to make `matches' more equitable, I propose to abolish `sets' and make a `match' consist of `games'. Thus instead of `best of 11 games = set; best of 5 sets = match' (i.e. he who first wins 6 games wins a set; he who first wins 3 sets wins a match), where a player may win with as few as 18 games, and must win with 28, I would substitute `he who first wins 28 games, or who gets 18 games ahead, wins the match.' I therefore propose as follows: `For a whole-day, he who first wins 28 games, or who gets 18 ahead, wins the match: for a half-day, he who first wins 14 games, or who gets 9 ahead, wins the match.'

TABLE I. (Pairs.)
I.(e) II.(m) (e) III.(m) (e) IV.(m) (e) V.(m) (e)
A}* A} C}* C} C} M} M}* R}* J}*
B} C}* G} M}* V}* f} f} f} f}
C}* E M}* V J}* J}* J} J}
D} G}* R} f}* a} V} R}*
E}* J} V}* A} L} R}*
F} M}* Y} J}* g}* g}
G}* P} a} G} R}*
H} R}* f}* L}* c}
J}* S} A}* R}*
K} V}* E} S}
L} W} J}* Y}
M}* Y}* P} a}*
N} a}* L}* g}*
P}* c} Q} T}
Q} f}* S}* c}
R}* g} W}
S}* B}* Z}
T} D} c}*
U} F}* g}*
V}* H} B}
W}* K} F}
X} L}* T}*
Y}* N} d}*
Z} Q}* h}
a}* T}*
b} U}
c}* X}
d} Z}*
e} b}
f}* d}*
g}* e}
h} h}*

TABLE II. (Superiors.)
I.(e) II.(m) (e) III.(m) (e) IV.(m) (e) V.(m) (e)
A ... C ... J(M)
B A (C) g()
C ... ... ... M V(f)
D C B(A)
E ... G A(C)
F E (G) T
G ... ... C L(M)
H G F(E)
J ... M ... ... ... ... R ... Pr.III.
K J L(M)
L M ... ... ... g(f)
M ... ... ... ... ... ... Pr.I.
N P Q(R)
P ... R J(M)
Q R ... L(M)
R ... ... M ... ... ... ... Pr.II.
S ... V ... R(f)
T S (V) ... g
U V T(S)
V ... ... ... f ... J(M)
W ... Y S(V)
X W Z(Y)
Y ... ... V a(f)
Z Y ... c(V)
a ... ... f ... J(M)
b a d(c)
c ... a (f) ... R
d c (a) (f)
e f h(g)
f ... ... ... ... ... ... M R J
g ... f ... ... ... R(M)
h g (f) d

6. Concluding remarks.

Let it not be supposed that, in thus proposing to make these Tournaments a game of pure skill (like chess) instead of a game of mixed skill and chance (like whist), I am altogether eliminating the element of luck, and making it possible to predict the prize-winners, so that no one else would care to enter. The `chances of the board' would still exist in full force: it would not at all follow, because a Player was reputed best, that he was certain of the 1st prize: a thousand accidents might occur to prevent his playing best: the 4th best, 5th best, or even a worst Player, need not despair of winning even the 1st prize.

Nor, again, let it be supposed that the present system, which allows an inferior player a chance of the 2nd prize, even though he fails to play above his reputation, is more attractive than one which, in such a case, gives him no hope. Let us compare the two systems, as to the attractions they hold out to (say) the 5th best Player in a Tournament of 32, with 3 prizes. The present system says, `If you play up to your reputation, your chance of a prize is about ¼th; and even if, by great luck and painstaking, you play 2nd or 3rd best, it never rises above a half.' My system says, `It is admitted that, if you only play up to your reputation, you will get nothing: but, if you play 2nd or 3rd best, you are certain of the proper prize.' Thus, the one system offers a chance of ¼th, where the other offers nothing; and a chance of a half, where the other offers certainty, I am inclined to think the second the more attractive of the two.

If, however, it be thought that, under the proposed system, the very inferior Players would feel so hopeless of a prize that they would not enter a Tournament, this can easily be remedied by a process of handicapping, as is usual in races, &c. This would give every one a reasonable hope of a prize, and therefore a sufficient motive for entering.

The proposed form of Tournament, though lasting a shorter time than the present one, has a great many more contests going on at once, and consequently furnishes the spectacle-loving public with a great deal more to look at.

THE ALPHABET-CIPHER

EXPLANATION

EACH column of this table forms a dictionary of symbols representing the alphabet: thus, in the A column, the symbol is the same as the letter represented; in the B column, A is represented by B, B by C, and so on.

To use the table, some word or sentence should be agreed on by two correspondents. This may be called the `key-word', or `key-sentence', and should be carried in the memory only.

In sending a message, write the key-word over it, letter for letter, repeating it as often as may be necessary: the letters of the key-word will indicate which column is to be used in translating each letter of the message, the symbols for which should be written underneath: then copy out the symbols only, and destroy the first paper. It will now be impossible for any one, ignorant of the key-word, to decipher the message, even with the help of the table.

For example, let the key-word be vigilance, and the message `meet me on Tuesday evening at seven', the first paper will read as follows --

v i g i l a n c e v i g i l a n c e v i g i l a n c e v i
m e e t m e o n t u e s d a y e v e n i n g a t s e v e n
h m k b x e b p x p m y l l y r x i i q t o l t f g z z v

The second will contain only `h m k b x e b p x p m y l l y r x i i q t o l t f g z z v'.

The receiver of the message can, by the same process, retranslate it into English.

N.B. -- If this table be lost, it can easily be written out from memory, by observing that the first symbol in each column is the same as the letter naming the column, and that they are continued downwards in alphabetical order. Of course it would only be necessary to write out the particular columns required by the key-word: such a paper, however, should not be preserved, as it would afford means for discovering the key-word.

CHRONOLOGICAL LIST OF THE WORKS IN THIS VOLUME
c. 1848 Crundle Castle. (The Rectory Umbrella, M.S. First published 1953.)
c. 1850 The Walking Stick of Destiny. (The Rectory Umbrella, M.S. First published 1932.)
c. 1850 A Hemispherical Problem. (The Rectory Umbrella, M.S. First published 1898.)
c. 1850 The Two Clocks. (The Rectory Umbrella, M.S. First published 1898.)
c. 1850-53 Lays of Sorrow. (The Rectory Umbrella, M.S. First published 1898.)
c. 1850-53 Prologue to `La Guida di Bragia'. (M.S. First published 1931.)
1853 The Two Brothers. (Mischmasch, M.S. First published 1899.)
1853 Solitude. The Train. March 1856.
1854 The Lady of the Ladle. The Whitby Gazette. 31 Aug. 1854.
1854 Wilhelm von Schmitz. The Whitby Gazette. 7 Sept. 1854.
1855 Stanza of Anglo-Saxon Poetry. (Mischmasch, M.S. First published 1898.)
1855 Theme with Variations. The Comic Times, 18 Aug. 1855.
1855 `She's all my fancy painted him'. The Comic Times, 8 Sept. 1855.
1855 Hints on Etiquette. The Comic Times, 13 Oct. 1855.
1855 Photography Extraordinary. The Comic Times, 3 Nov. 1855.
1855 The Palace of Humbug. The Oxford Critic, 29 May 1857.
1855 Ye Carpette Knighte. The Train, March 1856.
1856 The Path of Roses. The Train, May 1856.
1856 Novelty and Romancement. The Train, Oct. 1856.
1856 `Upon the Lonely Moor'. The Train, Oct. 1856.
1856 The Three Voices. The Train, Nov. 1856.
1857 The Sailor's Wife. The Train, April 1857.
1857 Where Does the Day Begin? The Illustrated London News, 18 April 1857.
1857 Hiawatha's Photographing. The Train, Dec. 1857.
1857-8 Melancholetta. College Rhymes, March 1862.
1858 The Legend of Scotland. (First published in The Lewis Carroll Picture Book, 1899.)
1859 The Willow Tree. Phantasmagoria, 1869.
1859 A Visit to Tennyson. Strand Magazine, May 1901.
1860 A Photographer's Day Out. South Shields Amateur Magazine, 1860.
1860 Faces in the Fire. All the Year Round, 11 Feb. 1860.
1860 Rules for Court Circular.
1860 A Valentine. Phantasmagoria, 1869.
1860 A Sea Dirge. College Rhymes, Nov. 1860.
1861 After Three Days. Temple Bar, July 1861.
1861 Three Sunsets (originally `The Dream of Fame'). College Rhymes, 1861.
1861 Ode to Damon. College Rhymes, Nov. 1861.
1861 The Horrid Hurdy-gurdies. College Rhymes, Nov. 1861.
1861 Endowment of the Greek Professorship.
1861 Acrostic: `Little Maidens, when you look'. Phantasmagoria, 1869.
1862 Miss Jones. (First published in Collected Verse, 1932.)
1862 Rules for Court Circular. (Second edition, revised.)
1862 `Only a Woman's Hair'. College Rhymes, March 1862.
1862 Disillusionized. College Rhymes, June 1862.
1862 Stolen Waters. College Rhymes, June 1862.
1862 Poeta Fit, Non Nascitur. College Rhymes, June 1862.
1862 The Lang Coortin'. College Rhymes, Nov. 1862.
1862 Beatrice. College Rhymes, Nov. 1862.
1862-3 Alice's Adventures Underground (published in this form in 1886).
1863 Croquet Castles.
1863 The Majesty of Justice. College Rhymes, March 1863.
1863 Size and Tears. College Rhymes, June 1863.
1864 Examination Statute.
1865 New Method of Evaluation.
1865 The Dynamics of a Parti-cle.
1865 Alice's Adventures in Wonderland.
1866 To M.A.B. (First published in Collected Verse, 1932.)
1866 The Elections to the Hebdomedal Council.
1867 Acrostic: `There was an ancient city . . .' Phantasmagoria 1869.
1867 Atalanta in Camden Town. Punch, 27 July 1867.
1867 Castle Croquet. Aunt Judy's Magazine, Aug. 1867.
1867 Bruno's Revenge. Aunt Judy's Magazine, Dec. 1867.
1867 The Deserted Parks.
1867 Christmas Greetings from a Fairy to a Child. Phantasmagoria, 1869.
1867 Tour in 1867 (Russian Journal). First printed 1928.
1868 The Valley of the Shadow of Death. Phantasmagoria, 1869.
1868 The Offer of the Clarendon Trustees.
1868 The Alphabet Cipher.
1868 The Woodstock Election. Oxford University Herald, 24 Nov. 1868.
1869 Phantasmagoria, and Other Poems.
1869 Preface to The Guildford Gazette Extraordinary, 29 Dec. 1869.
1869 `Three little maidens weary of the rail'. (Collingwood's Lewis Carroll, 1898.)
1869 `I sing a place wherein agree'. (Centenary Catalogue, 1932.)
1869 `When Mary and Ina . . .' (Some Rare Carrolliana, 1924.)
1870 `Two little girls near London dwell'. (Collingwood, 1898.)
1870 Puzzles from Wonderland. Aunt Judy's Magazine, Dec. 1870.
1871 Solutions to Puzzles from Wonderland. Aunt Judy's Magazine, Jan. 1871.
1871 `Three children -- their names are so fearful'. (Some Rare Carrolliana, 1924.)
1871 Prologue to Loan of a Lover, etc. (Williams and Madan, Handbook, 1931.)
1871 To all Child-Readers of Alice.
1871 Through the Looking-Glass. (Dated 1872.)
1872 The New Belfry of Christ Church, Oxford.
1872 `Two thieves went out to steal'. (Sotheby's Catalogue, 1929: Collected Verse, 1932.)
1873 The Vision of the Three T's.
1873 Prologue to Checkmate. (Strand Magazine, April 1898.)
1873 `Three little maids one winter day'. (Collingwood, 1898.)
1874 The Blank Cheque.
1874 Notes by an Oxford Chiel. (Collection of six Oxford pamphlets.)
1875 Vivisection as a Sign of the Times. Pall Mall Gazette, 12 Feb. 1875.
1875 Some Popular Fallacies About Vivisection. Fortnightly Review, 1 June 1875.
1876 The Hunting of the Snark.
1876 An Easter Greeting to Every Child who Loves Alice.
1876 Fame's Penny Trumpet.
1876 Acrostic: `Are you deaf, Father William?' (Collingwood, 1898.)
1876 Acrostic: `Maidens, if you love the tale'. (Sotheby Catalogue, 1929: Collected Verse, 1932.)
1876 Acrostic: `Love-lighted eyes, that will not start'. (Lewis Carroll Picture Book, 1899.)
1876 Acrostic: `Maiden, though thy heart may quail'. (Privately printed, 1930: Collected Verse 1932.)
1876 Acrostic: `Even while the blinding bandage lies'. (Quaritch Catalogue, 1949: Diaries, 1953.)
1876 Acrostic: `From the air do they come'. (Harcourt Amory Catalogue, 1932.)
1877 Madrigal: `He shouts amain!' (Lewis Carroll Centenary Catalogue, 1932.)
1877 Riddle: `The air is bright with hues of light'. Rhyme? and Reason?, 1883.
1878 Charade: `My first is singular at best' Rhyme? and Reason?, 1883.
1878 Love Among the Roses. (Lewis Carroll Picture Book, 1899.)
1878 Acrostic: `Around my lonely hearth tonight'. (Collingwood, 1898.)
1878 Answer to the White Queen's Riddle. Fun, 30 Oct. 1878.
1878-9 Doublets. (first called `Word-links'). Vanity Fair, 29 March 1879, and various separate editions, the final form being included in this volume.
1879-81 Lanrick. (Three variants, the final, separate edition included in this volume.)
1879 Riddle: `Empress of Art, for thee 1 twine'. Rhyme? and Reason?, 1883.
1880-85 A Tangled Tale (Serialised in The Monthly Packet. In book form, 1885.)
1880 To Rachel Daniel: `Oh pudgy, podgy pup'. (William and Madan, Handbook, 1931.)
1881 To Rachel Daniel: `What hand may wreathe thy natal crown'. Garland of Rachel, 1881.
1881 The Lyceum: `It is the lawyer's daughter'. (Lewis Carroll Picture Book, 1899.)
1881-2 Mischmasch. The Monthly Packet, June 1881; Nov. 1882.
c. 1882 Acrostic: `Round the wondrous globe'. (Collingwood, 1898).
c. 1882 Acrostic: `Maidens, if a maid you meet'. (Collingwood, 1898).
1882 Dreamland. Aunt Judy's Magazine, July 1882.
1883 Echoes. Rhyme? and Reason?, 1883.
1883 A Game of Fives. Rhyme? and Reason?, 1883.
1883 Rhyme? and Reason?
1883 Lawn Tennis Tournaments.
1884 Twelve Months in a Curatorship.
1884 Feeding the Mind. (First published in 1907.)
1885 To My Pupil. A Tangled Tale, 1885. (See 1880 above.)
1886 To My Child-Friend. The Game of Logic, 1886.
1886 `Who Will Riddle Me the How and the Why?' Preface to Alice's Adventures Underground. (See 1862-3 above.)
1886 Three Years in a Curatorship.
1887 Alice on the Stage. The Theatre, April 1887.
1887 Children in Theatres. The St. James's Gazette, 19 July 1887.
1888 The Stage and the Spirit of Reverence. The Theatre, June 1888.
1888 A Lesson in Latin. The Jabberwock, June 1888.
1888 Isa's Visit to Oxford. (Isa Bowman's Story of Lewis Carroll, 1899.)
1889 Sylvie and Bruno.
1889 A Nursery Darling. Dedication to The Nursery Alice, 1889.
1889 Stage Children. The Sunday Times, 4 Aug. 1889.
1889 Maggie's Visit to Oxford. (Isa Bowman's Story of Lewis Carroll, 1899.)
1890 Eight or Nine Wise Words about Letter-Writing.
1891 `Written by Maggie B--' (Maggs Catalogue, 1931; Collected Verse, 1932.)
1891 A Postal Problem.
1891 Puck Lost and Found. Three Sunsets, 1898.
1891 Syzygies. The Lady, 30 July 1891, and separately.
1893 Sylvie and Bruno Concluded.
1893 Syzygies and Lanrick (Final versions, as included in this volume.)
1894 Rules for Co-operative Backgammon. The Times, 6 March 1894.
1894 A Logical Paradox. Mind, July 1894.
1894 What the Tortoise Said to Achilles. Mind, Dec. 1894.
1895 Eternal Punishment. (Lewis Carroll Picture Book, 1899.)
1896 Resident Women Students.
1896 Preface to new edition of Through the Looking-Glass, 1897.
1897 A Magic Number. Chatterbox, Feb. 1897.
1897 Address for Children. St. Mary Magdalen Church Magazine, Oct. 1897.
1897 Introduction to The Lost Plum Cake, 1897.
1897 Preface to new edition of Alice's Adventures in Wonderland, 1898.

BIBLIOGRAPHY

(This list does not include pamphlets and articles)

BOOKS BY `LEWIS CARROLL'

Alice's Adventures in Wonderland, 1865.
Phantasmagoria, and Other Poems, 1869.
Through the Looking-Glass, and What Alice Found There, 1872.
The Hunting of the Snark, 1876.
Doublets -- a Word Puzzle, 1879.
Rhyme? and Reason?, 1883.
A Tangled Tale, 1885.
The Game of Logic, 1886.
Alice's Adventures Underground, 1886.
The Nursery Alice, 1889.
Sylvie and Bruno, 1889.
Syzygies and Lanrick, 1893.
Sylvie and Bruno Concluded, 1893.
Symbolic Logic, Part I, 1896.
Three Sunsets, and Other Poems, 1898.
The Lewis Carroll Picture Book, 1899.
Feeding the Mind, 1907.
The Rectory Umbrella and Mischmasch, (1849-62), 1932.
The Collected Verse of Lewis Carroll, 1932.
A Selection of Letters from Lewis Carroll to his Child-Friends, 1933.
The Russian Journal, and Other Selections, 1935.
The Diaries of Lewis Carroll, 1953.
Useful and Instructive Poetry, (1845), 1954.

BOOKS BY `C.L. DODGSON', OR ANONYMOUS

The Fifth Book of Euclid treated Algebraically, 1858.
A Syllabus of Plane Algebraical Geometry, 1860.
Notes on the First Two Books of Euclid, 1860.
A Guide to the Mathematical Student, 1864.
Condensation of Determinants, 1866.
Elementary Treatise on Determinants, 1867.
The Enunciations of Euclid I -- VI, 1873.
Notes by an Oxford Chiel, 1874.
Examples in Arithmetic, 1874.
Euclid Books I and II, 1875.
Euclid and his Modern Rivals, 1879.
The Principles of Parliamentary Representation, 1884.
Supplement to `Euclid and his Modern Rivals', 1885.
Curiosa Mathematica, I: A New Theory of Parallels, 1888.
Curiosa Mathematica, II: Pillow-Problems, 1893.

BOOKS ABOUT LEWIS CARROLL

The Life and Letters of Lewis Carroll. By S. Dodgson Collingwood, 1898.
The Story of Lewis Carroll. By Isa Bowman. 1899.
Lewis Carroll in Wonderland and at Home. By Belle Moses. 1910.
A Bibliography of the Writings of Lewis Carroll. By S.H. Williams. 1924.
A Handbook of the Literature of the Rev. C.L. Dodgson. By S.H. Williams and Falconer Madan. 1931. Supplement, 1935.
The Life of Lewis Carroll. By Langford Reed. 1932.
The Lewis Carroll Centenary in London. By Falconer Madan. 1932.
Carroll's Alice. By Harry Morgan Ayres. 1936.
Victoria through the Looking-Glass. By Florence Becker Lennon. 1945. Revised as The Life of Lewis Carroll, 1962.
The Story of Lewis Carroll. By Roger Lancelyn Green. 1949.
Lewis Carroll -- Photographer. By Helmut Gernsheim. 1949.
The White Knight: A Study of C.L. Dodgson. By Alexander L. Taylor. 1952.
The Diaries of Lewis Carroll: Now first Edited and Supplemented by Roger Lancelyn Green. 1953.
Lewis Carroll. By Derek Hudson. 1954.
Swift and Carroll. By Phyllis Greenacre. 1955.
Lewis Carroll: A Bodley Head Monograph. By Roger Lancelyn Green. 1960.
The Annotated Alice. By Martin Gardner. 1960.

The Lewis Carroll Handbook. The Handbook by Williams and Madan revised with numerous additions, and brought up to 1960. By Roger Lancelyn Green. 1962.

ACKNOWLEDGMENTS

A Tour in 1867 from A Russian Journal edited by John Francis McDermott and published by E.P. Dutton & Co. Inc.

© John Francis McDermott 1935 -- by permission of the executors of the late Lewis Carroll and Messrs Dutton.

Crundle Castle from The Diaries of Lewis Carroll by permission of the executors of the late Lewis Carroll, Mr. Roger Lancelyn Green, Messrs Cassell & Co. Ltd and the Oxford University Press Inc.

The Walking Stick of Destiny from The Rectory Umbrella and Other Stories by permission of the executors of the late Lewis Carroll and Messrs Cassell & Co. Ltd.



1 I have not thought it necessary to reproduce here the glossary of words which may be used to form links. The preface will give a sufficiently clear idea of the classes of words which are not admissible.

1The best way is to imagine yourself walking round with the sun and asking the inhabitants as you go, `What morning is this?' If you suppose them living all the way around, and all speaking one language, the difficulty is obvious.

1This is clearly an impossible case, and is only put as an hypothesis.

2The usual exclamation at waking, generally said with a yawn.

3`If all the world were apple pie, And all the sea were ink, And all the trees were bread and cheese, What should we have to drink?'
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