HMMT 二月 2002 · 团队赛 · 第 1 题
HMMT February 2002 — Team Round — Problem 1
题目详情
- For every board configuration with strictly fewer than k blank squares, the first player wins 1 with probability strictly greater than ; but 2
解析
- [15] Determine the number of palindromes that are less than 1000. Solution. Every one-digit number (there are nine) is a palindrome. The two-digit palindromes have the form a a for a nonzero digit a , so there are nine of them. A three-digit palindrome is a b a with a a nonzero digit and b any digit, so there are 9 × 10 = 90 of these. Thus the number of palindromes less than 1000 is 9 + 9 + 90 = 108 .