Newspaper article The Christian Science Monitor

Math Chat: Halloween Cards, Sprinklers, & Mirrors

Newspaper article The Christian Science Monitor

Math Chat: Halloween Cards, Sprinklers, & Mirrors

Article excerpt

Old Halloween challenge

Ralph Thomas proposes a new card game for you and an opponent for Halloween. Each hand, a goblin deals both players a certain number of cards. The highest card wins (e.g., ace beats king, two aces tie). If you win you get two points; if your opponent wins he gets just one point. (You have an advantage.)

Do you prefer to use a regular deck, a double deck, or a pinochle deck (which has two of each card from 9 on up to ace)? How many cards would you like the goblin to deal out each hand? Do you prefer four or eight hands in the tournament? Answer In the winning answer, Stephen Jabloner writes: "If I were playing that Halloween card game, I'd opt for one regular deck, one card per hand, and eight hands in the tournament. Each of these choices is based on the notion that I want as few ties as possible since I have an advantage when someone wins. "A single regular deck is less likely to end in a tie game than either a double deck or a pinochle deck. For example, if I hold one card from a regular deck, there's only a 3/51 (5.9 percent) chance that my opponent will tie me, whereas there is a 7/103 (6.8 percent) chance with a double deck and 7/47 (14.9 percent) chance with a pinochle deck." Similarly, the more cards dealt, the more likely a tie. If the goblin deals out all the cards, there is a good chance we will both have an ace and tie. Finally, the longer the tournament, the less likely my opponent will win by a fluke. More on sprinklers Although most readers agreed with the published answer that an underwater sprinkler sucking in water will not turn, Erik Randolph for example argues that conservation of momentum requires that if the water in the sprinkler is going one way, the sprinkler must turn the other way. Leaf Turner points out that this backwards effect, much smaller than that due to all the water spurting out in normal sprinkler operation, and almost undetectable, has been measured in experiments with a special, nearly frictionless sprinkler. …

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