HMMT 二月 2018 · COMB 赛 · 第 1 题
HMMT February 2018 — COMB Round — Problem 1
题目详情
- Consider a 2 × 3 grid where each entry is one of 0, 1, and 2. For how many such grids is the sum of the numbers in every row and in every column a multiple of 3? One valid grid is shown below. [ ] 1 2 0 2 1 0
解析
- Consider a 2 × 3 grid where each entry is one of 0, 1, and 2. For how many such grids is the sum of the numbers in every row and in every column a multiple of 3? One valid grid is shown below. [ ] 1 2 0 2 1 0 Proposed by: Henrik Boecken Answer: 9 2 Any two elements in the same row fix the rest of the grid, so 3 = 9.