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Winning openings in rectangular Chomp

Can a rectangular Chomp board have at least three winning first moves? Chomp is the chocolate-bar removal game with one poisoned corner; strategy stealing proves a nontrivial rectangle is winning without identifying which first moves win.

Why it matters and what counts as progress

Why it matters: Strategy stealing establishes a winner without identifying a move; counting winning openings asks for finer finite-game information.

What counts as progress: Find a board with three winning openings and certify their outcomes by exact game-state analysis.

How the problem developed

  1. 20 Mar 2019 · Problem statement [1]

    Thotsaporn Thanatipanonda, reporting Doron Zeilberger and Shalosh B. Ekhad's challenge Recorded the second computational Chomp challenge: find a rectangular bar with at least three winning opening moves.

  2. 11 Aug 2026 · Solution [2]

    Jaideep Sai Padhi with a large language model Reported a bar with three winning openings and proved a staircase constraint on winning openings for every Chomp bar.

AI contribution

Sources

  1. Thanatipanonda, Introduction: It Is Impossible to Solve Chomp(?)
  2. Padhi, Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics
  3. Padhi, Solutions to Five Challenge Problems in Enumerative and Algorithmic Combinatorics
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