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A,B,C,D Letter Puzzle

Date: 08/30/2002 at 16:14:31
From: Meaghan Stewart
Subject: Impossible math problem

Can you place the letters A,B,C,D in the chart below so that no 
letter appears twice in any new row, column, or diagonal?

THE CHART


___/_____/______/_______

___/_____/______/______

___/_____/______/______

___/_____/______/______


Date: 08/30/2002 at 22:52:24
From: Doctor Peterson
Subject: Re: Impossible math problem

Hi, Meaghan.

Never call a problem "impossible"; it usually turns out to be easy. 
All you need here is an orderly way to try out possibilities. Note 
that each row must contain one of each letter, so you can fill in one 
row at a time.

You can start by placing the first row, and then marking places where 
A can't be placed in other rows:

    A B C D
    x x . .
    x . x .
    x . . x

Now there are only two places to put A in the second row, so we can 
place them and again mark where A can't be put:

    A B C D    A B C D
    x x A x    x x x A
    x . x .    x . x x
    x . x x    x . . x

You can fill in the remaining A's in only one way for each case. Then 
use the same kind of thinking in each of these pictures to find where 
D can go, then B and C.

If you need more help, please write back and show me how far you got.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
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