The Canterbury Puzzles

Henry Ernest Dudeney (1857–1930 or perhaps 1847–1930 — both occur in the book) was the preeminent English mathematical puzzle-maker of his day. The Canterbury Puzzles appeared in 1907. It contains the often-repeated spider-and-fly problem that he devised in 1903, about the minimum distance, along its surfaces, between two points in a rectangular prism and his also often-repeated dissection of a square that, if hinged, can be folded into an equilateral triangle. (You can buy a piece of furniture based on it that can be square or triangular as you please. Who said that recreational mathematics has no applications?) It does not contain the first example, SEND + MORE = MONEY, of the problem to replace letters with digits so that the addition is true, because he didn’t think of it until 1924. He was consistently original. His chief rival, the American Sam Loyd (1841–1911), though better than Dudeney at chess, was no match for him mathematically.

It was a different time, those days before television, radio, and movies, not to mention computers. People, then as now, had the need to be entertained, and some of them satisfied it, partially at least, with mathematical puzzles. Many magazines, then an important entertainment medium, had regular mathematical puzzle sections. (Lewis Carroll’s A Tangled Tale appeared in installments in The Monthly Packet magazine between 1880 and 1885.) Part of The Canterbury Puzzles is a description of the fictional Squire Davidge’s puzzle party, where each guest presented a puzzle to be solved. Something like that may have existed in Dudeney’s day (he had to get the idea from somewhere) but mathematical puzzle parties no longer exist. Pick a magazine at random and you will find no recreational mathematics in it. We have easier ways to slake our thirst for entertainment.

The book contains 114 problems. The title comes from Chaucer: Dudeney has Chaucer’s pilgrims present puzzles that, of course, Dudeney made up. This gives him the opportunity to indulge in pseudo-medieval language (“I trow there not be one among ye,” quoth the Nun …) that is, according to your taste, amusing, irrelevant, or annoying. It was the fashion of the day to dress puzzles up. Dudeney continues the process in later sections, e.g., “Puzzling Times in Solvamhall Castle”. (Did readers in 1907 find that as wince-worthy as I do now? Probably not.)

Most of the problems will be too difficult for the average reader. No one is going to find two positive rational numbers besides 1 and 2 whose cubes sum to 9. Dudeney’s numerators and denominators have twelve digits each. He must have been so proud of them (“nobody has ever published the much smaller result that I now print”) that he couldn’t resist making a problem — Number 20, The Puzzle of the Doctor of Physic — whose solution they were. Not many readers will hit on the solution of the problem to put ten sugar cubes in three cups so that each cup contains an odd number of cubes (put seven cubes in one cup, two in the second, one in the third, and then place the third cup in the second). The problems require no algebra, trigonometry, or advanced mathematics: incredible ingenuity suffices for solutions.

But that’s what the solutions section, more than half as large as the problems section, is for. We can see and appreciate the ingenuity. We can also appreciate the numerous drawings — period pieces, they are now — by an uncredited illustrator.

Is the book worth buying now? My answer may be influenced by the affection I have for it (I bought it more than fifty years ago), but I think that it is. It’s good reading.

Woody Dudley retired from teaching in 2004 and no longer has to solve the puzzles of student behavior.