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Square Squares Settlement (Posted on 2014-07-30) Difficulty: 3 of 5
What is the smallest number of straight lines with which you can make precisely 225 squares?

For example with five vertical and six horizontal lines, evenly spaced, 40 squares are formed: twenty 1x1, twelve 2x2, six 3x3 and two 4x4.
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No Solution Yet Submitted by K Sengupta    
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Solution Upper bound? | Comment 1 of 2

I think I found a solution with 20 lines. 

Make a 10x7 grid of squares.  This creates 224 squares (70 of size 1x1, 54 of size 2x2, ... , 4 of size 7x7).  You can then extend the sides of length 7 so that they are length 10, and connect them to form one more square of size 10x10.

http://i.imgur.com/x7gdjIb.png

Not sure if that's the minimum, though. 


  Posted by tomarken on 2014-07-31 10:03:41
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