Hints and solutions to
Problem of the day for Thursday, January 9
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How many squares in this picture?
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There are more squares than meet the eye at first!
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We can organize this by looking at squares of different sizes.
First, there are certainly 16 little (i.e., 1x1) squares.
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Next we need to look for 2x2 squares. There are three of these
in a row, and there are three rows of them, so there are nine 2x2
squares.
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Next, there are four 3x3 squares (can you find them?).
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And finally, there is one 4x4 square (the whole thing).
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So altogether there are 16 + 9 + 4 + 1 =
30 squares in the picture.
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Do you see a pattern here that can be generalized?