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Omni-MATH / Let n and k be positive integers. Cathy is playing the following game. There are n marbles and k boxes, with the marbles labelled 1 to n. Initially, all marbles are placed inside o…

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problem

Let nn and kk be positive integers. Cathy is playing the following game. There are nn marbles and kk boxes, with the marbles labelled 1 to nn. Initially, all marbles are placed inside one box. Each turn, Cathy chooses a box and then moves the marbles with the smallest label, say ii, to either any empty box or the box containing marble i+1i+1. Cathy wins if at any point there is a box containing only marble nn. Determine all pairs of integers (n,k)(n, k) such that Cathy can win this game.
Plain-text mathematical notation (without MathML)
Let n and k be positive integers. Cathy is playing the following game. There are n marbles and k boxes, with the marbles labelled 1 to n. Initially, all marbles are placed inside one box. Each turn, Cathy chooses a box and then moves the marbles with the smallest label, say i, to either any empty box or the box containing marble i+1. Cathy wins if at any point there is a box containing only marble n. Determine all pairs of integers (n,k) such that Cathy can win this game.
Original LaTeX notation
Let $n$ and $k$ be positive integers. Cathy is playing the following game. There are $n$ marbles and $k$ boxes, with the marbles labelled 1 to $n$. Initially, all marbles are placed inside one box. Each turn, Cathy chooses a box and then moves the marbles with the smallest label, say $i$, to either any empty box or the box containing marble $i+1$. Cathy wins if at any point there is a box containing only marble $n$. Determine all pairs of integers $(n, k)$ such that Cathy can win this game.

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Source and history

task_id
88409e74-df45-5bd8-9a0c-62f39eb8879f
task_key
test--88409e74-df45-5bd8-9a0c-62f39eb8879f
task_revision_id
1
config / split
/ test

Official source

initial import