396.--A MATCH MYSTERY.

Here is a little game that is childishly simple in its conditions. But
it is well worth investigation.

Mr. Stubbs pulled a small table between himself and his friend, Mr.
Wilson, and took a box of matches, from which he counted out thirty.

"Here are thirty matches," he said. "I divide them into three unequal
heaps. Let me see. We have 14, 11, and 5, as it happens. Now, the two
players draw alternately any number from any one heap, and he who draws
the last match loses the game. That's all! I will play with you, Wilson.
I have formed the heaps, so you have the first draw."

"As I can draw any number," Mr. Wilson said, "suppose I exhibit my usual
moderation and take all the 14 heap."

"That is the worst you could do, for it loses right away. I take 6 from
the 11, leaving two equal heaps of 5, and to leave two equal heaps is a
certain win (with the single exception of 1, 1), because whatever you do
in one heap I can repeat in the other. If you leave 4 in one heap, I
leave 4 in the other. If you then leave 2 in one heap, I leave 2 in the
other. If you leave only 1 in one heap, then I take all the other heap.
If you take all one heap, I take all but one in the other. No, you must
never leave two heaps, unless they are equal heaps and more than 1, 1.
Let's begin again."

"Very well, then," said Mr. Wilson. "I will take 6 from the 14, and
leave you 8, 11, 5."