HMMT 二月 2006 · GEN2 赛 · 第 7 题
HMMT February 2006 — GEN2 Round — Problem 7
题目详情
- What is the smallest positive integer n such that n and ( n + 1) both contain the digit 7 but ( n + 2) does not?
解析
- What is the smallest positive integer n such that n and ( n + 1) both contain the digit 2 7 but ( n + 2) does not? Answer: 27 Solution: The last digit of a square is never 7. No two-digit squares begin with 7. There are no 3-digit squares beginning with the digits 17, 27, 37, or 47. In fact, the 2 smallest square containing the digit 7 is 576 = 24 . Checking the next few numbers, 2 2 2 2 2 we see that 25 = 625, 26 = 676, 27 = 729, 28 = 784, and 29 = 841, so the answer is 27.