HMMT 十一月 2024 · THM 赛 · 第 1 题

HMMT November 2024 — THM Round — Problem 1

Compute the number of ways to fill each of the 12 empty cells in the grid on the T right with one of T , A , L , or C such that each of the four rows, columns, and A bolded 2 × 2 square regions contains each letter exactly once. L C

解析

Compute the number of ways to fill each of the 12 empty cells in the grid below with one of T , A , L , or C such that each of the four rows, columns, and bolded 2 × 2 square regions contains each letter exactly once. T A L C Proposed by: Arul Kolla, Katelyn Zhou Answer: 2 Solution: T ? A L C Consider the cell marked with a ?. It may be replaced with either an L or a C , each of which leads to a unique filling of the grid. The answer is 2 , shown below: T C A L T L C A L A C T C A T L C T L A A C L T A L T C L T A C Note that they are symmetric with respect to reflection about the diagonal.