MathDB
Rook with limited movement

Source: Kvant Magazine No. 9 2022 M2715

March 8, 2023
Kvantcombinatoricsboard

Problem Statement

A lame rook lies on a 9×99\times 9 chessboard. It can move one cell horizontally or vertically. The rook made nn{} moves, visited each cell at most once, and did not make two moves consecutively in the same direction. What is the largest possible value of nn{}?
From the folklore