The Puzzle Art of Lewis Carroll

In the arts, there is a longstanding tradition of identifying the masterpieces—the great novels, the great symphonies, the great paintings—as the most illuminating things to admire and study. Puzzledom too has its masterpieces and its great artists. Arguably, one of the greatest of all time was Lewis Carroll, who devised puzzles from all domains of human intelligence, from language and logic to mathematics and geometry.

I have dealt with some of Carroll’s puzzles in previous blogs. Here, I wish to present five of his masterpieces. Needless to say, he created so many ingenious puzzles that it would be brazenly presumptuous to claim that I have chosen his five best. In reality, I have chosen five that I believe truly exemplify what a puzzle is and how it produces thinking of diverse kinds, following up on my previous blog in which I attempted to define a puzzle cognitively.

Most people know Lewis Carroll, the nom de plume of Charles Lutwidge Dodgson, as the writer of children’s books, especially Alice’s Adventures in Wonderland and Through the Looking-Glass, and What Alice Found There. Two of his other books, titled Pillow Problems (1880) and A Tangled Tale (1885), contain truly ingenious and challenging mind-benders, many of which have been recycled in various versions and variations in puzzle collections ever since.

Carroll was fascinated by the inquisitive and fanciful (ludic) imagination of children. Alice’s Adventures contains all sorts of puzzles involving ingenious mind play and double-entendre that have amused and challenged children ever since the book was first published. He was especially captivated by the ability of puzzles to impose a peculiar kind of ordered thinking on the erratic and capricious human mind. Finding solutions to puzzles does indeed provide an internal sense of order.

Five Classic Examples

1. This puzzle was found in the notes that Carroll sent to Professor Bartholomew Price, who was his mathematics tutor:

Imagine that you have some wooden cubes. You also have six paint tins each containing a different colour of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours? Remember that two cubes are different only when it is not possible, by turning one, to make it correspond with the other.

2. Carroll was the inventor and master of the doublet puzzle. I have covered this puzzle genre in previous blogs. To reiterate here, the goal is to evolve one word into the other of two given words, by changing only one letter at a time, forming a legitimate new word with each change. As a trivial example, change WE to MA (colloquial term for “mother”) in the least number of links. Only one link (me) in between the two words is required: WE—me—MA.

Carroll created the following doublet (among others) as a competition piece for an 1879 issue of Vanity Fair:

Turn POOR into RICH in the least number of links.

3. The following is Carroll’s version of the classic river-crossing puzzle, devised by the eighth century English cleric, scholar, and adviser to Charlemagne, Alcuin (c. 735–804). He included it in a letter he wrote to someone called Jessie Sinclair to pass on to his sister Sally. Below is a paraphrase:

A man had a fox, a goose, and a bag of corn. He had to get them over a river, but the boat that was there was so tiny that he could only take one across at a time; and he couldn’t ever leave the fox and the goose together, for then the fox would eat the goose; and if he left the goose and the corn together, the goose would eat the corn. How does he get them all across safely?

4. Carroll was a master at wordplay. Here is a riddle he wrote in his diary for June 30, 1982. It seems intractable but, in typical Carrollian fashion, there is a deceptively simple answer:

A Russian had three sons.

The first, named Rab, became a lawyer.

The second, named Ymra, became a soldier.

The third became a sailor: what was his name?

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5. Finally, here is one of Carroll’s trickier doublets.

Place BEANS on SHELF in the least number of links.

Answers

1. Thirty cubes.

This is an ingenious puzzle in combinatorics. A cube has six faces. Let’s represent them with a, b, c, d, e, and f. When face a is opposite face b, there are six arrangements for the remaining four colors around the cube: cdef, cdfe, cedf, cefd, cfde, and cfed. Similarly, with face a opposite face c, there are also six arrangements for the remaining four colors around the cube: bdef, bdfe, bedf, befd, bfde, and bfed. The same reasoning applies to face a opposite face d, face a opposite face e, and face a opposite face f—all having six arrangements for the remaining four colors. In sum, there are 5 possible opposite face combinations: (1) face a opposite face b; (2) face a opposite face c; (3) face a opposite face d; (4) face a opposite face e; and (5) face a opposite face f. For each of these, 6 arrangements of the remaining colors around the cube can be made. In total: 5 × 6 = 30 arrangements. This means that 30 cubes will be needed if they are to be painted distinctively.

2. Five links are required

POOR—boor—book—rook—rock—rick—RICH

[Note that rick can mean either “pile” or “strain”]

3. Here are the seven required trips:

(1) Take the goose over

(2) Return

(3) Take the corn over

(4) Return with the goose

(5) Leave the goose and take the fox over

(6) Return

(7) Take the goose over

4. Yvan

By spelling each name backward, we get the profession. So, RAB spelled backward is BAR, and as we are told Rab became a lawyer (entered the Bar). YMRA spelled backward is ARMY, hence the fact that Ymra became a soldier. Thus, NAVY is the backward spelling for YVAN. The third son’s name was Yvan, who became a sailor.

5. Seven links are required:

BEANS—beams—seams—shams—shame—shale—shall—shell—SHELF