benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Given an m×n table consisting of mn unit cells. Alice and Bob play the following game: Alice goes first and the one who moves colors one of the empty cells with one of the given th…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Given an m×nm \times n table consisting of mnmn unit cells. Alice and Bob play the following game: Alice goes first and the one who moves colors one of the empty cells with one of the given three colors. Alice wins if there is a figure, such as the ones below, having three different colors. Otherwise Bob is the winner. Determine the winner for all cases of mm and nn where m,n≥3m, n \ge 3.
Plain-text mathematical notation (without MathML)
Given an m×n table consisting of mn unit cells. Alice and Bob play the following game: Alice goes first and the one who moves colors one of the empty cells with one of the given three colors. Alice wins if there is a figure, such as the ones below, having three different colors. Otherwise Bob is the winner. Determine the winner for all cases of m
and n where m,n≥3.
Original LaTeX notation
Given an $m \times n$ table consisting of $mn$ unit cells. Alice and Bob play the following game: Alice goes first and the one who moves colors one of the empty cells with one of the given three colors. Alice wins if there is a figure, such as the ones below, having three different colors. Otherwise Bob is the winner. Determine the winner for all cases of $m$
and $n$ where $m, n \ge 3$.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
1795a83b-c590-5ea9-83c0-d8c969d0ec07
task_key
test--1795a83b-c590-5ea9-83c0-d8c969d0ec07
task_revision_id
1
config / split
/ test

Official source

initial import