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 100 squares (Posted on 2006-04-30)
What is the fewest straight lines with which you can make exactly 100 squares?

For example with four vertical and five horizontal lines, evenly spaced, 20 squares are formed: twelve 1x1, six 2x2 and two 3x3.

``` _____
|_|_|_|
|_|_|_|
|_|_|_|
|_|_|_|```

 See The Solution Submitted by Jer Rating: 4.0000 (3 votes)

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 re: solution and discussion ==> A general formula | Comment 5 of 6 |
(In reply to solution and discussion by Charlie)

For a rectangle m*n , i.e. m+1 by n+1 lines the number of squares can be obtained from the following formula:

N=1/6*n(n+1)*(3m-n+1)

This equation can be easily obtained by evaluation and simplification of

SUM ( (m-i)*(n-i))  taken over   i=0 to i=n-1

Edited on May 3, 2006, 12:47 am
 Posted by Ady TZIDON on 2006-05-03 00:46:22

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