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Omni-MATH / In this problem assume s₁=3 and s₂=2. Determine, with proof, the nonnegative integer k with the following property: 1. For every board configuration with strictly fewer than k blan…

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problem

In this problem assume s1=3s_{1}=3 and s2=2s_{2}=2. Determine, with proof, the nonnegative integer kk with the following property: 1. For every board configuration with strictly fewer than kk blank squares, the first player wins with probability strictly greater than 12\frac{1}{2}; but 2. there exists a board configuration with exactly kk blank squares for which the second player wins with probability strictly greater than 12\frac{1}{2}.
Plain-text mathematical notation (without MathML)
In this problem assume s₁=3 and s₂=2. Determine, with proof, the nonnegative integer k with the following property: 1. For every board configuration with strictly fewer than k blank squares, the first player wins with probability strictly greater than (1)/(2); but 2. there exists a board configuration with exactly k blank squares for which the second player wins with probability strictly greater than (1)/(2).
Original LaTeX notation
In this problem assume $s_{1}=3$ and $s_{2}=2$. Determine, with proof, the nonnegative integer $k$ with the following property: 1. For every board configuration with strictly fewer than $k$ blank squares, the first player wins with probability strictly greater than $\frac{1}{2}$; but 2. there exists a board configuration with exactly $k$ blank squares for which the second player wins with probability strictly greater than $\frac{1}{2}$.

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Source and history

task_id
8bb801d0-baba-51c4-969f-91b14290ae24
task_key
test--8bb801d0-baba-51c4-969f-91b14290ae24
task_revision_id
1
config / split
/ test

Official source

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