The (almost really) Complete Works of Lewis Carroll

§ 1. Definitions

Def. 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

[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.]

Def. 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.”

Def. 3

In a “Syzygy-Problem,” two words are given, which are to form the end-words 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

Def. 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.]

Def. 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 versâ.

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.

[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.

[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 “0*”.

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.]

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:—

then the Score = $$(a+2b)+(m+1).(m+2)-(2l+w).]$$

§ 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

[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

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

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

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 4 letters. ‘Came.’ That must be something ending in ‘cament,’ I fancy. That gives ‘predicament’, and ‘medicament’: I ca’n’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:—

“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 wo’n’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 ‘redarn 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:—

“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 ungentle reader is a lusus naturæ 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.

§ 6. Solutions of the Problems

The appended dates refer to the Nos. of ‘The Lady’ in which these solutions appeared.