THE CANTERBURY PUZZLES
give solutions for any number of cheeses with three stools, for
triangular numbers with four stools, and for pyramidal numbers with
five stools. In these cases there is always only one method of solu-
tion—that is, of piling the cheeses.
In the case of three stools, the first and fourth rows tell us that
4 cheeses may be removed in 15 moves, 5 in 31, 7 in 127. The
second and fifth rows show that, with four stools, 10 may be re-
moved in 49, and 21 in 321 moves. Also, with five stools, we find
from the third and sixth rows that 20 cheeses require 111 moves,
and 35 cheeses 351 moves. But we also learn from the table the
necessary method of piling. Thus with four stools and 10 cheeses,
the previous column shows that we must make piles of 6 and 3, which
will take 17 and 7 moves respectively; that is we first pile the 6
smallest cheeses in 17 moves on one stool ; then we pile the next 3
cheeses on another stool in 7 moves ; then remove the largest cheese
in 1 move ; then replace the 3 in 7 moves ; and finally replace the
6 in 17—making in all the necessary 49 moves. Similarly we are
told that with five stools 35 cheeses must form piles of 20, 10 and 4,
which will respectively take 111, 49 and 15 moves.
If the number of cheeses in the case of four stools is not triangular,
and in the case of five stools
pyramidal, then there will
be more than one way of
making the piles and sub-
sidiary tables will be re-
quired. This is the case
with the Reve's 8 cheeses.
But I will leave the reader
to work out for himself the
extension of the problem.
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(JP 2.-
The Pardoners Puzzle.
The diagram will show
how the Pardoner started
from the large black town and visited all the other towns once,
and once only, in fifteen straight pilgrimages.
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