been done,
with the exception of the two diagonals, which so far have baffled all
efforts. But it is not certain that it cannot be done.

Though the contents of the present volume are in the main entirely
original, some very few old friends will be found; but these will not, I
trust, prove unwelcome in the new dress that they have received. The
puzzles are of every degree of difficulty, and so varied in character
that perhaps it is not too much to hope that every true puzzle lover will
find ample material to interest--and possibly instruct. In some cases I
have dealt with the methods of solution at considerable length, but at
other times I have reluctantly felt obliged to restrict myself to giving
the bare answers. Had the full solutions and proofs been given in the
case of every puzzle, either half the problems would have had to be
omitted, or the size of the book greatly increased. And the plan that I
have adopted has its advantages, for it leaves scope for the mathematical
enthusiast to work out his own analysis. Even in those cases where I have
given a general formula for the solution of a puzzle, he will find great
interest in verifying it for himself.

THE CANTERBURY PUZZLES

[Illustration]

A Chance-gathered company of pilgrims, on their way to the shrine of
Saint Thomas a Becket at Canterbury, met at the old Tabard Inn, later
called the Talbot, in Southwark, and the host proposed that they should
beguile the ride by each telling a tale to his fellow-pilgrims. This we
all know was the origin of the immortal _Canterbury Tales_ of our great
fourteenth-century poet, Geoffrey Chaucer. Unfortunately, the tales were
never completed, and perhaps that is why the quaint and curious
"Canterbury Puzzles," devised and propounded by the same body of
pilgrims, were not also recorded by the poet's pen. This is greatly to be
regretted, since Chaucer, who, as Leland tells us, was an "ingenious
mathematician" and the author of a learned treatise on the astrolabe, was
peculiarly fitted for the propounding of problems. In presenting for the
first time some of these old-world posers, I will not stop to explain the
singular manner in which they came into my possession, but proceed at
once, without unnecessary preamble, to give my readers an opportunity of
solving them and testing their quality. There are certainly far more
difficult puzzles extant, but difficulty and interest are two qualities
of puzzledom that do not nece