SOLUTIONS
THE CANTERBURY PUZZLES
1.—
The Reves Puzzle.
The 8 cheeses can be removed in 33 moves ; 10 cheeses in 49
moves; and 21 cheeses in 321 moves. I will give my general
method of solution in the cases of 3, 4 and 5 stools.
Write out the following table to any required length :—
1 Stools.
3
4
5
3
4
5
Number of Cheeses.
123 4 5 6 7
I 3 6 io 15 21 28
1 4 10 20 35 56 84
Number of Moves.
1
3 7
J
5 3
1
63 127
1 5 17 49 129 321 769
1 7 31 in 351 1023 2815
The first row contains the natural numbers. The second row is
found by adding the natural numbers together from the beginning.
The numbers in the third row are obtained by adding together the
numbers in the second row from the beginning. The fourth row
contains the successive powers of 2, less 1. The next series is
found by doubling in turn each number of that series and adding
the number that stands above the place where you write the result.
The last row is obtained in the same way. This table will at once
131
K 2
