Even Odds
A bag contains 16 billiard balls, some white and some black. You draw two balls at the same time. It is equally likely that the two will be the same color as different colors. What is the proportion of colors within the bag?
Black and White
Vision Thing
A puzzle from Lewis Carroll:
A king wishes to dismiss his wise men, but he must obey an old law that says there must always be:
Seven blind of both eyes,
Ten blind of one eye,
Five that see with both eyes,
Nine that see with one eye.
How many wise men must he keep?
Black and White
The British Chess Magazine reprinted this “amusing old timer” in 1892. “We suspect that the amusement will be caused by the rapidity of solving it, and the prettiness and surprise of the mating position.” White to mate in two moves.
Pool Party
A billiard ball is resting on a table that measures 10 feet by 5 feet. A player hits it with no “English” and it strikes four different cushions and returns to its starting point. University of Alberta mathematician Murray Klamkin asks: How far did it travel?
Black and White
By Sam Loyd. White is kicking himself — he has just completed a move, and realizes that he could have given mate instead. What was his move, and what was the mate?
Signs and Portents
In the November 1971 issue of Word Ways, reader Solomon Golomb noted that the following placard appeared in the window of a business establishment “and was considered quite ordinary by all passers-by.” Why?
Treasure Island
Babylas, Hilary, and Sosthenes have escaped the tower and divided their treasure into three bags. But now they must cross a river, and the boat can accommodate only two men at a time, or one man and a bag. None will trust another with his bag on the shore, but they agree that a man in the boat can be trusted to drop or retrieve a bag at either shore, as he’ll be too busy to tamper with it. How can they cross the river?
Down and Out
Three robbers, Babylas, Hilary, and Sosthenes, are stealing a treasure chest from the top of an old tower. Unfortunately, they’ve had to destroy their ladder to avoid pursuit, so they’ll have to descend using a crude tackle — a single pulley and a long rope with a basket at each end.
Babylas weighs 170 pounds, Hilary 100 pounds, Sosthenes 80 pounds, and the treasure 60 pounds. If the difference in weight between the two baskets is greater than 20 pounds then the heavier basket will descend too quickly and injure its occupant (though the treasure chest can withstand this). How can the three of them safely escape the tower with the treasure?
