Brain Workout

Challenging puzzles to sharpen your mind, improve your memory, and keep your brain fit.

The Doublet Puzzle: A Masterpiece from the Pen of Lewis Carroll

Can you solve one of Lewis Carroll's doublets?

imageMost people probably know Lewis Carroll, the nom de plume of Charles Lutwidge Dodgson, as the author of Alice's Adventures in Wonderland and Through the Looking-Glass, and What Alice Found There.

He was also an eminent mathematician, who wrote important works in the field, such as A Syllabus of Plane Algebraical Geometry and Euclid and His Modern Rivals. But to a puzzle fanatic Carroll is regarded as one of the greatest puzzle-makers of all time, if not the greatest. His Pillow Problems and A Tangled Tale, for example, contain puzzles that have become classics, being used in various disguises, variations, and elaborations in puzzle anthologies ever since.

One of Carroll's puzzle unquestioned masterpieces is the doublet, which he introduced through the pages of Vanity Fair in March of 1879. He likely took the name for his puzzle from the witches' incantation in Macbeth: "Double, double, toil and trouble." The doublet asks us to transform a given word into another by changing only one letter at a time, forming a genuine new word (not a proper name) with each letter change. The puzzle seems simple enough, but it really isn't, as new solvers soon discover. For example, can you turn HEAD into TAIL? The solution involves five letter changes, producing four "links" between HEAD and TAIL.

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HEAD
heal (Results from changing the "d" of "head" to "l")
teal (Results from changing the "h" of "heal" to "t")
tell (Results from changing the "a" of "teal" to "l")
tall (Results from changing the "e" of "tell" to "l")
TAIL (Results from changing the first "l" of "tall" to "i")

By the way, this is the original doublet puzzle devised by Carroll for Vanity Fair. The doublet became an instant craze in London. In 1879, the publisher Macmillan assembled the puzzles in Vanity Fair into a booklet titled Doublets: A Word Puzzle, which sold out quickly, being followed by two other editions containing more puzzles each time. Try your hand at the following doublets, taken mainly from this collection.

1. Can you evolve APE into MAN with just four links?
2. Make FLOUR into BREAD with five links.
3. Go from SLEEP to DREAM with five links.
4. Increase ONE to TWO with six links.
5. Turn BLACK into WHITE with six links.
6. Make GRASS GREEN with six links.
7. Turn BLUE into PINK with eight links.
8. Can you get from RIVER to SHORE with 10 links?
9. Can you transform a WITCH into a FAIRY with 12 links?

Carroll later modified the rules to make the puzzles more difficult. Here is the example he used to introduce a new version of the doublet: Change IRON into LEAD by introducing a new letter or by rearranging the letters of the word at any step. You may not do both in the same step.

IRON
icon (Results from changing the "r" in "iron" to "c")
coin (Results from rearranging the letters in "icon")
corn (Results from changing the "i" in "coin" to "r")
cord (Results from changing the "n" in "corn" to "d")
lord (Results from changing the "c" in "cord" to "l")
load (Results from changing the "r" in "lord" to "a")
LEAD (Results from changing the "o" in "load" to "e")

Now, try your hand at this kind of doublet.

10. Change HATE into VEIL with three links.

The doublet has cropped up in a number of unexpected settings. For example, the mad narrator in Vladimir Nabokov's novel Pale Fire recalls playing the doublet game, which he calls "word golf." Here is Nabokov's puzzle. Can you solve it?

11. Change LASS to MALE with three links.

Biologist John Maynard Smith constructed the following doublet in his essay titled "The Limitations of Molecular Evolution." Can you come up with the solution?

12. Change WORD to GENE with three links.

In his classic word puzzle collection, Language on Vacation (1965), Dimitri Borgmann claimed that the ideal form of the doublet puzzle was the one that involved the transformation of n letters in n moves. He renamed the puzzle a word ladder. An example would be to change COLD to WARM. There are four letters in the two words and, thus, an "ideal" solution is one that will consist of four changes, which means inserting three links between the words, with the fourth change producing WARM:

COLD
cord
card
ward
WARM

Other versions have been devised over the years. One of these is to create a link by adding a letter to a previous word: A simple example would be to change BAD to BEARD with one link:

BAD
bard (Results from inserting "r" into "bad")
BEARD (Results from inserting "e" into "bard")

Here are a few of this type for you to solve:

13. Change TO to STOOL with two links, adding a letter at each step.
14. Change ON to STONED with three links, adding a letter at each step.

The counterpart to the additive doublet is the subtractive doublet, whereby you have to take away a letter from a previous word to create the link. Try these.

15. Change BEAST to BE with two links, subtracting a letter at each step.
16. Change SPRINT to IN with three links, subtracting a letter at each step.

One can also have doublets consisting of a combination of the above rules. Let me add two new variations for the fun of it. The first is to alternate between adding and subtracting letters. So, if you add a letter to one link, then you must subtract a letter from the link you have constructed to create the link after it.

17. Change LEVER to VEER with four links, using the above rules.
18. Change STOP to PEN with four links, also using the above rules.

A second variation is to provide a synonym or antonym for a link (no matter how many letters you produce in the process). For example, a synonym for BAD is EVIL and an antonym for EVIL is GOOD. So, this part of the word ladder would look like this: BAD-evil-good. You are not told how many of each type (synonym or antonym) are required or in what order. These are tough!

19. Change TALL to CHILD with four links by using a synonym or antonym at a step, as required.
20. Change BRIGHT to SMOOTH with four links again by using a synonym or antonym at a step, as required.

As a final word on doublets, I would like to suggest that solving them will give the verbal areas of the brain a veritable workout. The reason I believe this to be the case is that a solution entails knowledge of both word structure and semantics. The main semantic process involved is word association and, thus, recall, which is a powerful form of brain-activating thinking, at least as I read the relevant research. We are of course faced with the usual problem of trying to understand or explain how the research translates into benefits through puzzle-solving. The way I look at it is that puzzles such as the doublet can only be beneficial to overall brain health. As one's semantic memory begins to wane through the aging process, giving the semantic parts of the brain a puzzle workout can only be advantageous. You can get more doublet puzzles at wordchains.com and you can even download a program to help you create your own puzzles at ihsan.biz/word.html#wordladderDesc.

Answers
1. APE-apt-opt-oat-mat-MAN (This is Howard Gardner's solution; Carroll's solution had five links.)
2. FLOUR-floor-flood-blood-brood-broad-BREAD
3. SLEEP-bleep-bleed-breed-bread-dread-DREAM
4. ONE-ope (poetic form of "open")-opt-out-tut-tot-too-TWO
5. BLACK-blank-blink-clink-chink-chine (an animal backbone)-whine-WHITE
6. GRASS-crass-cress (a plant of the cabbage family)-tress-trees-treed-greed-GREEN
7. BLUE-glue-glut-gout-pout-port-part-pant-pint-PINK
8. RIVER-rover-cover-coves-cores-corns-coins-chins-shins-shine-shone-SHORE
9. WITCH-winch (lifting device)-wench-tench (a freshwater fish of the minnow family)-tenth-tents-tints-tilts-tills-fills-falls-fails-fairs-FAIRY
10. HATE-have (new letter)-hive (new letter)-live (new letter)-VEIL (rearrangement)
11. LASS-mass-mast-malt-MALE
12. WORD-wore-gore-gone-GENE
13. TO-too-tool-STOOL
14. ON-ton-tone-stone-STONED
15. BEAST-best-bet-BE
16. SPRINT-print-pint-pin-IN
17. LEVER-ever (subtract "l")-every (add "y")-very (subtract the first "e")-veery (add "e") (a woodland thrush)-VEER (subtract "y")
18. STOP-top (subtract "s")-tope (add "e") (a small grayish shark)-ope (subtract "t") (poetic form for "open")-open (add "n")-PEN (subtract "o")
19. TALL-short (antonym for "tall")-little (synonym for "short")-big (antonym for "little")-adult (synonym for "big")-CHILD (antonym for "adult")
20. BRIGHT-dull (antonym for "bright")-sharp (antonym for "dull")-blunt (antonym for "sharp")-flat (synonym for "blunt")-SMOOTH (synonym for "flat")

 

 

Marcel Danesi, Ph.D., is a professor of semiotics and anthropology at Victoria College, University of Toronto. His books include The Puzzle Instinct and The Total Brain Workout.

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