MathDB

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

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.

Problem Statement