Math Forum - Problem of the Week

Squares in a Square

[Spanish version]

Curtis was explaining to Ian that his teacher told him to find all the squares in a 50x50 checkerboard. He said, "I started with smaller checkerboards and when I got to the 4x4 checkerboard I found 30 different squares." Ian said, "I think that was a good way to start. Now let's see if we can spot a pattern."

Question: If you have a checkerboard that is 50x50 with small squares inside it, how many squares will there be altogether?

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