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IberoAmerican
2019 IberoAmerican
5
5
Part of
2019 IberoAmerican
Problems
(1)
2019 Iberoamerican Mathematical Olympiad P5
Source:
9/16/2019
Don Miguel places a token in one of the
(
n
+
1
)
2
(n+1)^2
(
n
+
1
)
2
vertices determined by an
n
×
n
n \times n
n
×
n
board. A move consists of moving the token from the vertex on which it is placed to an adjacent vertex which is at most
2
\sqrt2
2
away, as long as it stays on the board. A path is a sequence of moves such that the token was in each one of the
(
n
+
1
)
2
(n+1)^2
(
n
+
1
)
2
vertices exactly once. What is the maximum number of diagonal moves (those of length
2
\sqrt2
2
) that a path can have in total?
combinatorics