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covering a ladder (part of a grid) with n squares

Source: Mexican Mathematical Olympiad 2006 P4

July 31, 2018
combinatoricsgrid

Problem Statement

For which positive integers nn can be covered a ladder like that of the figure (but with nn steps instead of 44) with nn squares of integer sides, not necessarily the same size, without these squares overlapping and without standing out from the edge of the figure ?
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