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HMMT 十一月 2013 · 冲刺赛 · 第 20 题

HMMT November 2013 — Guts Round — Problem 20

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 11 ] There exist unique nonnegative integers A, B between 0 and 9, inclusive, such that
    (1001 · A + 110 · B ) = 57 , 108 , 249 .2
    Find 10 · A + B .
解析

英文解析

  1. [ 11 ] There exist unique nonnegative integers A, B between 0 and 9, inclusive, such that
    (1001 · A + 110 · B ) = 57 , 108 , 249 .2
    Find 10 · A + B .
    2 2
    Answer: 75 We only need to bound for AB 00; in other words, AB ≤ 5710 but ( AB + 1) ≥ 5710.
    A quick check gives AB = 75. (Lots of ways to get this...)