What a lame rook
Source: 44th International Tournament of Towns, Senior O-Level P5, Fall 2022
February 16, 2023
combinatoricsdominoesboardTournament of Towns
Problem Statement
A board is covered by non-overlapping dominos of size. A lame rook (which can only move one cell at a time, horizontally or vertically) has visited each cell once on its route across the board. Call a move by the rook longitudinal if it is a move from one cell of a domino to another cell of the same domino. What is:[*]the maximum possible number of longitudinal moves?
[*]the minimum possible number of longitudinal moves?