HMMT 十一月 2018 · THM 赛 · 第 2 题
HMMT November 2018 — THM Round — Problem 2
题目详情
- Consider the addition problem: C A S H
- M E O S I D E where each letter represents a base-ten digit, and C, M, O 6 = 0. (Distinct letters are allowed to represent the same digit) How many ways are there to assign values to the letters so that the addition problem is true?
解析
- Consider the addition problem: C A S H
- M E O S I D E where each letter represents a base-ten digit, and C, M, O 6 = 0. (Distinct letters are allowed to represent the same digit) How many ways are there to assign values to the letters so that the addition problem is true? Proposed by: James Lin Answer: 0 Clearly, CASH and M E cannot add up to 11000 or more, so O = 1 and S = 0. By examining the units digit, we find that H = 0. Then CASH + M E < 9900 + 99 < 10000, so there are no solutions.