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HMMT 十一月 2016 · 冲刺赛 · 第 30 题

HMMT November 2016 — Guts Round — Problem 30

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 15 ] On the blackboard, Amy writes 2017 in base- a to get 133201 . Betsy notices she can erase a digitafrom Amy’s number and change the base to base- b such that the value of the the number remains the same. Catherine then notices she can erase a digit from Betsy’s number and change the base to base- csuch that the value still remains the same. Compute, in decimal, a + b + c .
    HMMT November 2016, November 12, 2016 — GUTS ROUND
    Organization Team Team ID#
解析

英文解析

  1. [ 15 ] On the blackboard, Amy writes 2017 in base- a to get 133201 . Betsy notices she can erase a digitafrom Amy’s number and change the base to base- b such that the value of the the number remains the same. Catherine then notices she can erase a digit from Betsy’s number and change the base to base- csuch that the value still remains the same. Compute, in decimal, a + b + c .
    Proposed by: Daniel Qu
    Answer: 22
    2017 = 133201 = 13201 = 1201
    4 6 12