by Dudeney, Henry Ernest, 1857-1930
Available in 215 free installments
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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?
395.?A WAR PUZZLE GAME.
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.
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 p 9 119 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."
397.?THE MONTENEGRIN DICE GAME.
It is said that the inhabitants of Montenegro have a little dice game that is both ingenious and well worth investigation. The two players first select two different pairs of odd numbers (always higher than 3) and then alternately toss three dice. Whichever first throws the dice so that they add up to one of his selected numbers wins. If they are both successful in two successive throws it is a draw and they try again. For example, one player may select 7 and 15 and the other 5 and 13. Then if the first player throws so that the three dice add up
7 or 15 he wins, unless the second man gets either 5 or 13 on his throw.
The puzzle is to discover which two pairs of numbers should be selected in order to give both players an exactly even chance.
398.?THE CIGAR PUZZLE.
