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### 174 Game

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Date: 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

- Doctor Terrel, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Puzzles
Middle School Puzzles

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