MathDB

On a

(4n + 2)\times (4n + 2)

square grid, a turtle can move between squares sharing a side.The turtle begins in a corner square of the grid and enters each square exactly once, ending in the square where she started. In terms of

n

, what is the largest positive integer

k

such that there must be a row or column that the turtle has entered at least

k

distinct times?

Problem Statement