proved to be an old enemy of Mr. Mowbray's, was convicted on other
evidence that was discovered; but before he paid the penalty for his
wicked act, he admitted that Mr. Slyman's statement of the time was
perfectly correct.

Can you also give the exact time?

113.--_Cutting a Wood Block._

An economical carpenter had a block of wood measuring eight inches long
by four inches wide by three and three-quarter inches deep. How many
pieces, each measuring two and a half inches by one inch and a half by
one inch and a quarter, could he cut out of it? It is all a question of
how you cut them out. Most people would have more waste material left
over than is necessary. How many pieces could you get out of the block?

114.--_The Tramps and the Biscuits._

Four merry tramps bought, borrowed, found, or in some other manner
obtained possession of a box of biscuits, which they agreed to divide
equally amongst themselves at breakfast next morning. In the night, while
the others were fast asleep under the greenwood tree, one man approached
the box, devoured exactly a quarter of the number of biscuits, except the
odd one left over, which he threw as a bribe to their dog. Later in the
night a second man awoke and hit on the same idea, taking a quarter of
what remained and giving the odd biscuit to the dog. The third and fourth
men did precisely the same in turn, taking a quarter of what they found
and giving the odd biscuit to the dog. In the morning they divided what
remained equally amongst them, and again gave the odd biscuit to the
animal. Every man noticed the reduction in the contents of the box, but,
believing himself to be alone responsible, made no comments. What is the
smallest possible number of biscuits that there could have been in the
box when they first acquired it?

[Illustration]

SOLUTIONS

THE CANTERBURY PUZZLES

1.--_The Reve's 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:--

Stools. Number of Cheeses.

3 1 2 3 4 5 6 7 Natural Numbers.
4 1 3 6 10 15 21 28 Triangular Numbers.
5 1 4 10 20 35 56 84 Triangular Pyramids.

Number of Moves.

3 1 3 7 15 31 63 127
4 1 5 17 49 129 321 769
5