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Part of 2016 Chile National Olympiad

Problems(1)

giraffe chess piece

Source: 2016 Chile National Olympiad level 2 p3

The giraffe is a chess piece that moves

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squares in one direction and then a box in a perpendicular direction. What is the smallest value of

n

such that the giraffe that starts from a corner on an

n \times n

board can visit all the squares of said board?