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Omni-MATH / The numbers 1,2,…,10 are randomly arranged in a circle. Let p be the probability that for every positive integer k<10, there exists an integer k^{prime}>k such that there is at mos…

Problem

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problem

The numbers 1,2,…,101,2, \ldots, 10 are randomly arranged in a circle. Let pp be the probability that for every positive integer k<10k<10, there exists an integer $k^{\prime}>k$ such that there is at most one number between kk and $k^{\prime}$ in the circle. If pp can be expressed as ab\frac{a}{b} for relatively prime positive integers aa and bb, compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
The numbers 1,2,…,10 are randomly arranged in a circle. Let p be the probability that for every positive integer k<10, there exists an integer $k^{\prime}>k$ such that there is at most one number between k and $k^{\prime}$ in the circle. If p can be expressed as (a)/(b) for relatively prime positive integers a and b, compute 100a+b.
Original LaTeX notation
The numbers $1,2, \ldots, 10$ are randomly arranged in a circle. Let $p$ be the probability that for every positive integer $k<10$, there exists an integer $k^{\prime}>k$ such that there is at most one number between $k$ and $k^{\prime}$ in the circle. If $p$ can be expressed as $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$, compute $100 a+b$.

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Source and history

task_id
963553ea-5d1a-5016-89df-efe4d518fba9
task_key
test--963553ea-5d1a-5016-89df-efe4d518fba9
task_revision_id
1
config / split
/ test

Official source

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