benchmarks.wiki / Public workspace
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Omni-MATH / Two players play a game, starting with a pile of N tokens. On each player's turn, they must remove 2^(n) tokens from the pile for some nonnegative integer n. If a player cannot mak…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
Two players play a game, starting with a pile of tokens. On each player's turn, they must remove tokens from the pile for some nonnegative integer . If a player cannot make a move, they lose. For how many between 1 and 2019 (inclusive) does the first player have a winning strategy?
Plain-text mathematical notation (without MathML)
Two players play a game, starting with a pile of N tokens. On each player's turn, they must remove 2^(n) tokens from the pile for some nonnegative integer n. If a player cannot make a move, they lose. For how many N between 1 and 2019 (inclusive) does the first player have a winning strategy?
Original LaTeX notation
Two players play a game, starting with a pile of \(N\) tokens. On each player's turn, they must remove \(2^{n}\) tokens from the pile for some nonnegative integer \(n\). If a player cannot make a move, they lose. For how many \(N\) between 1 and 2019 (inclusive) does the first player have a winning strategy?Discussion
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Source and history
- task_id
dcf97ac8-f5d5-503b-a468-d038cbe0d553- task_key
test--dcf97ac8-f5d5-503b-a468-d038cbe0d553- task_revision_id
- 1
- config / split
- / test
initial import