The Second Book of Mathematical Puzzles and Diversions

Henry Ernest Dudeney: England’s Greatest Puzzlist 33
articles for the English magazine Tit-Bits, and later they
arranged to exchange puzzles for their magazine and newspaper
columns. This may explain the large amount of duplication
in the published writings of Loyd and Dudeney.
Of the two, Dudeney was probably the better mathematician.
Loyd excelled in catching the public fancy with
manufactured toys and advertising novelties. None of
Dudeney’s creations had the world-wide popularity of Loyd’s
“14-15” puzzle or his “Get Off the Earth” paradox involving a
vanishing Chinese warrior. On the other hand, Dudeney’s
work was mathematically more sophisticated (he once
described the rebus or picture puzzle, of which Loyd produced
thousands, as a “juvenile imbecility” of interest only to the feeble-minded).
Like Loyd, he enjoyed clothing his problems
with amusing anecdotes. In this he may have had the assistance
of his wife Alice, who wrote more than 30 romantic novels
that were widely read in her time. His six books of puzzles
(three are collections assembled after his death in 1930)
remain unexcelled in the literature of puzzledom.
Dudeneys‘s first book, The Canterbury Puzzles, was published
in 1907. It purports to be a series of quaint posers propounded
by the same group of pilgrims whose tales were recounted
by Chaucer. “I will not stop to explain the singular manner in
which they came into my possession,” Dudeney writes, “but
[will] proceed at once….. to give my readers an opportunity of
solving them.” The haberdasher’s problem, found in this
book, is Dudeney’s best-known geometrical discovery. The
problem is to cut an equilateral triangle into four pieces that
can then be reassembled to form a square.
The drawing at upper left in Figure 12 shows how the cuts
are made. Bisect AB at D and BC at E. Extend AE to F so that
EF equals EB. Bisect AF at G, then, with G as the center,
describe the arc AHF. Extend EB to H. With E as the center,
draw the arc HJ. Make JK equal to BE. From D and K drop
perpendiculars on EJ to obtain points L and M.