174 GameDate: 08/16/2001 at 20:27:48 From: zhongwanting Subject: 174 Game Hello, Dr. Math! I have a question. Billy, Tom and Jack are playing a game. Tom and Jack are the players. Billy is the judge. The rule of the game is: the players announce numbers in turn. The numbers they announce should be within 1 to 8. The judge adds the numbers they announce. If the sum becomes 174 (or more than that) after one player's announcement, then that player wins. Billy decides to let Tom announce first. In order to win the game, which number should Tom announce first? I don't know how to start. It seems to me that perhaps every number from 1 to 8 is possible. Thanks a lot! Zhongwanting Date: 08/17/2001 at 19:34:57 From: Doctor Terrel Subject: Re: 174 Game Hello, This is a famous type of number game. There are many different versions, and once you know the secret, you can invent more ways to play. Rather than just tell you what Tom should say, I'll explain my favorite version and let you solve yours by yourself. In my version the goal to win is 100, and the numbers to add are anything from 1 to 10. Here Tom would say "1" to start, and would guarantee a win in the following way: If Billy says "5", Tom says "6" If Billy says "8", Tom says "3" If Billy says "2", Tom says "9" If Billy says "4", Tom says "7" and so on. Hint: add those two numbers in each line. Do you see a pattern? Eventually, Billy must make the total of 99. Then Tom just adds 1, and wins! Now, think hard about that game, then use the general idea to solve your own problem. - Doctor Terrel, The Math Forum http://mathforum.org/dr.math/ |
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