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.

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15 lines.

We start  with a 7x6 rectangle. This will contain 7x6+6x5+5x4+4x3+3x2+2x1=112 squares.

If we remove 2 1x1 squares which lie on opposite sides of the longer side we will be removing 12 squares (6 per square) leaving us with 100 squares.

Posted by Sparsh on 2006-05-11 13:14:43