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HMMT 二月 2016 · 冲刺赛 · 第 35 题

HMMT February 2016 — Guts Round — Problem 35

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 20 ] (Maximal Determinant) In a 17 × 17 matrix M , all entries are ± 1. The maximum possiblevalue of | det M | is N . Estimate N .
    ⌊ ⌋
    An estimate of E > 0 earns 20 min( N/E, E/N ) points.2
解析

英文解析

  1. [ 20 ] (Maximal Determinant) In a 17 × 17 matrix M , all entries are ± 1. The maximum possiblevalue of | det M | is N . Estimate N .
    ⌊ ⌋
    An estimate of E > 0 earns 20 min( N/E, E/N ) points.2
    Proposed by: Evan Chen
    Answer: 327680 · 216
    n 1
    This is Hadamard’s maximal determinant problem. There’s an upper bound of n which empirically 2
    seems to give reasonably good estimates, but in fact this is open for general n .