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2

Part of 2010 Paraguay Mathematical Olympiad

Problems(1)

Paraguayan National Olympiad 2010, Level 3, Problem 2

Source:

9/20/2014
A series of figures is shown in the picture below, each one of them created by following a secret rule. If the leftmost figure is considered the first figure, how many squares will the 21st figure have?
http://www.artofproblemsolving.com/Forum/download/file.php?id=49934
Note: only the little squares are to be counted (i.e., the 2×22 \times 2 squares, 3×33 \times 3 squares, …\dots should not be counted)
Extra (not part of the original problem): How many squares will the 21st figure have, if we consider all 1×11 \times 1 squares, all 2×22 \times 2 squares, all 3×33 \times 3 squares, and so on?.
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