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Omni-MATH / Esmeralda has created a special knight to play on quadrilateral boards that are…

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problem

Esmeralda has created a special knight to play on quadrilateral boards that are identical to chessboards. If a knight is in a square then it can move to another square by moving 1 square in one direction and 3 squares in a perpendicular direction (which is a diagonal of a 2×42\times4 rectangle instead of 2×32\times3 like in chess). In this movement, it doesn't land on the squares between the beginning square and the final square it lands on. A trip of the length nn of the knight is a sequence of nn squares C1,C2,...,CnC1, C2, ..., Cn which are all distinct such that the knight starts at the C1C1 square and for each ii from 11 to n−1n-1 it can use the movement described before to go from the CiCi square to the C(i+1)C(i+1). Determine the greatest N∈NN \in \mathbb{N} such that there exists a path of the knight with length NN on a 5×55\times5 board.
Plain-text mathematical notation (without MathML)
Esmeralda has created a special knight to play on quadrilateral boards that are identical to chessboards. If a knight is in a square then it can move to another square by moving 1 square in one direction and 3 squares in a perpendicular direction (which is a diagonal of a 2×4 rectangle instead of 2×3 like in chess). In this movement, it doesn't land on the squares between the beginning square and the final square it lands on.

A trip of the length n of the knight is a sequence of n squares C1,C2,...,Cn which are all distinct such that the knight starts at the C1 square and for each i from 1 to n−1 it can use the movement described before to go from the Ci square to the C(i+1).

Determine the greatest N∈N such that there exists a path of the knight with length N on a 5×5 board.
Original LaTeX notation
Esmeralda has created a special knight to play on quadrilateral boards that are identical to chessboards. If a knight is in a square then it can move to another square by moving 1 square in one direction and 3 squares in a perpendicular direction (which is a diagonal of a $2\times4$ rectangle instead of $2\times3$ like in chess). In this movement, it doesn't land on the squares between the beginning square and the final square it lands on.

A trip of the length $n$ of the knight is a sequence of $n$ squares $C1, C2, ..., Cn$ which are all distinct such that the knight starts at the $C1$ square and for each $i$ from $1$ to $n-1$ it can use the movement described before to go from the $Ci$ square to the $C(i+1)$.

Determine the greatest $N \in \mathbb{N}$ such that there exists a path of the knight with length $N$ on a $5\times5$ board.

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Source and history

task_id
4fa9d367-f22b-5c40-8ff3-cb455a9a2d08
task_key
test--4fa9d367-f22b-5c40-8ff3-cb455a9a2d08
task_revision_id
1
config / split
/ test

Official source

initial import