Amusements in Mathematics HTML version

This variation of the last puzzle is also played by two persons. One puts a counter on No.
6, and the other puts one on No. 55, and they play alternately by removing the counter to
any other number in a line. If your opponent moves at any time on to one of the lines you
occupy, or even crosses one of your lines, you immediately capture him and win. We will
take an illustrative game.
A moves from 55 to 52; B moves from 6 to 13; A advances to 23; B goes to 15; A
retreats to 26; B retreats to 13; A advances to 21; B retreats to 2; A advances to 7; B goes
to 3; A moves to 6; B must now go to 4; A establishes himself at 11, and B must be
captured next move because he is compelled to cross a line on which A stands. Play this
over and you will understand the game directly. Now, the puzzle part of the game is this:
Which player should win, and how many moves are necessary?
Here is another puzzle game. One player, representing the British general, places a
counter at B, and the other player, representing the enemy, places his counter at E. The
Britisher makes the first advance along one of the roads to the next town, then the enemy
moves to one of his nearest towns, and so on in turns, until the British general gets into
the same town as the enemy and captures him. Although each must always move along a
road to the next town only, and the second player may do his utmost to avoid capture, the
British general (as we should suppose, from the analogy of real life) must infallibly win.
But how? That is the question.
Here is a little game that is childishly simple in its conditions. But it is well worth
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