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### Squares Having a Common Side

```
Date: 03/08/99 at 08:57:27
From: suresh kumar
Subject: Probability

In choosing two squares from a chess board, what is the probability
that they have a common side?
```

```
Date: 03/08/99 at 16:25:11
From: Doctor Anthony
Subject: Re: Probability

There are 3 types of square:

(a) squares in the middle part that have 4 squares with common
borders

(b) corner squares (of which there are 4) that have 2 squares with a
common border

(c) edge squares, which have 3 squares with a common border

There are  36 type (a) squares.
4 type (b) squares.
24 type (c) squares.

Altogether there are 64 squares on the board.

The probability that two squares have a common border is then:

Prob(type a) x 4/63 + Prob(type b) x 2/63 + Prob(type c) x 3/63

=  36/64 x 4/63 + 4/64 x 2/63 + 24/64 x 3/63

36 x 4 + 4 x 2 + 24 x 3        224        1
=  -------------------------  =  ------  =  ----
64 x 63                4032       18

- Doctor Anthony, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Probability

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