## A MATCH MYSTERY.

(

Puzzle Games.)

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."

Mr. Stubbs then left 8, 11, 3; Mr. Wilson, 8, 5, 3; Mr. Stubbs, 6, 5, 3;

Mr. Wilson,4, 5, 3; Mr. Stubbs, 4, 5, 1; Mr. Wilson, 4, 3, 1; Mr.

Stubbs, 2, 3, 1; Mr. Wilson, 2, 1, 1; which Mr. Stubbs reduced to 1, 1,

1.

"It is now quite clear that I must win," said Mr. Stubbs, because you

must take 1, and then I take 1, leaving you the last match. You never

had a chance. There are just thirteen different ways in which the

matches may be grouped at the start for a certain win. In fact, the

groups selected, 14, 11, 5, are a certain win, because for whatever your

opponent may play there is another winning group you can secure, and so

on and on down to the last match."

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A WAR PUZZLE GAME.