THE CANTERBURY PUZZLES
But five out of eleven will only eat the pie, four will only eat the
pasty, and two are willing to eat of either. Any possible
combination must fall into one of the following groups, (i.) Where
the warden pie is distributed entirely among the five first mentioned,
(ii.) where only one of the accommodating pair is given pie, (iii.)
where the other of the pair is given pie, (iv.) where both of the
pair are given pie. The numbers of combinations are (i.) = 75, (ii.)
= 50, (iii.) = 10, (iv.) = 10, making in all 145 ways of selecting the
eight participants. A great many people will give the answer as
185, by overlooking the fact that in forty cases in class (iii.)
precisely the same eight guests would be sharing the meal as in class
(ii.), though the accommodating pair would be eating differently of the
two dishes. This is the point that upset the calculations of the
company.
16.—
The Sompnour s Puzzle,
The number that the Sompnour confided to the Wife of Bath was
twenty-nine, and she was told to begin her count at the Doctor of
Physic, who will be seen in the illustration standing the second on
her right. The first count of twenty-nine falls on the Shipman,
who steps out of the ring. The second count falls on the Doctor,
who next steps out. The remaining three counts fall respectively on
the Cook, the Sompnour, and the Miller. The ladies would,
therefore, have been left in possession had it not been for the
unfortunate error of the good Wife. Any multiple of 2,520 added
to 29 would also have served the same purpose, beginning the
count at the Doctor.
17.—
The Shipman s Puzzle.
There are just two hundred and sixty-four different ways in which
the ship
Magdalen
might have made her ten annual voyages
without ever going over the same course twice in a year. Every
year she must necessarily end her tenth voyage at the island from
which she first set out.
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