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HMMT 二月 2002 · 团队赛 · 第 1 题

HMMT February 2002 — Team Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. For every board configuration with strictly fewer than k blank squares, the first player winswith probability strictly greater than ; but 1 2

英文原题

The first player chooses s 1 subject to the constraint that 2 ≤ s 1 ≤ 5; then

解析

英文解析

  1. [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 palindromeshave the form a a for a nonzero digit a , so there are nine of them. A three-digit palindrome is a b awith a a nonzero digit and b any digit, so there are 9 × 10 = 90 of these. Thus the number ofpalindromes less than 1000 is 9 + 9 + 90 = 108 .