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Dotty Squares

Problem

By joining dots together, how many squares can you draw on a grid measuring 4 dots by 4 dots?


Solution

Consider the following diagrams.

So there would be 1 + 4 + 9 + 4 + 2 = 20 squares that can be drawn on a 4 times 4 grid.

What about 5 times 5 grids?

Can you generalise for any size grid?

Problem ID: 35 (Feb 2001)     Difficulty: 2 Star

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