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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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 Solution: spoiler | Comment 1 of 6

Fifteen lines: 8 horizontal, 7 vertical. Two of the vertical lines do not complete the length of the grid.  Creating 38 (1x1s), 28 (2x2s), 18 (3x3s), 10 (4x4s), 4 (5x5s), 2 (6x6s). Total: 100.

_ _ _ _ _ _
|_|_|_|_|_ _|
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|_|_|_|_|_|_|
|_|_|_|_|_|_|
|_|_|_|_|_|_|
|_ _|_|_|_|_|

Edited for format error.

Edited on April 30, 2006, 5:17 pm
 Posted by Leming on 2006-04-30 17:16:37

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