benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / On an infinite chessboard, a solitaire game is played as follows: at the start,…

Problem

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

problem

On an infinite chessboard, a solitaire game is played as follows: at the start, we have n2n^2 pieces occupying a square of side n.n. The only allowed move is to jump over an occupied square to an unoccupied one, and the piece which has been jumped over is removed. For which nn can the game end with only one piece remaining on the board?
Plain-text mathematical notation (without MathML)
On an infinite chessboard, a solitaire game is played as follows: at the start, we have n² pieces occupying a square of side n. The only allowed move is to jump over an occupied square to an unoccupied one, and the piece which has been jumped over is removed. For which n can the game end with only one piece remaining on the board?
Original LaTeX notation
On an infinite chessboard, a solitaire game is played as follows: at the start, we have $n^2$ pieces occupying a square of side $n.$ The only allowed move is to jump over an occupied square to an unoccupied one, and the piece which has been jumped over is removed. For which $n$ can the game end with only one piece remaining on the board?

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
beacfafa-b38e-5ccd-827c-f321ec277617
task_key
test--beacfafa-b38e-5ccd-827c-f321ec277617
task_revision_id
1
config / split
/ test

Official source

initial import