HMMT 二月 2024 · COMB 赛 · 第 2 题
HMMT February 2024 — COMB Round — Problem 2
题目详情
- A lame king is a chess piece that can move from a cell to any cell that shares at least one vertex with it, except for the cells in the same column as the current cell. A lame king is placed in the top-left cell of a 7 × 7 grid. Compute the maximum number of cells it can visit without visiting the same cell twice (including its starting cell).
解析
- A lame king is a chess piece that can move from a cell to any cell that shares at least one vertex with it, except for the cells in the same column as the current cell. A lame king is placed in the top-left cell of a 7 × 7 grid. Compute the maximum number of cells it can visit without visiting the same cell twice (including its starting cell). Proposed by: Arul Kolla Answer: 43 Solution: Color the columns all-black and all-white, alternating by column. Each move the lame king takes will switch the color it’s on. Assuming the king starts on a black cell, there are 28 black and 21 white cells, so it can visit at most 22 + 21 = 43 cells in total, which is easily achievable: