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Omni-MATH / Let N be a positive integer. Brothers Michael and Kylo each select a positive integer less than or equal to N, independently and uniformly at random. Let p_(N) denote the probabili…

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problem

Let NN be a positive integer. Brothers Michael and Kylo each select a positive integer less than or equal to NN, independently and uniformly at random. Let pNp_{N} denote the probability that the product of these two integers has a units digit of 0. The maximum possible value of pNp_{N} over all possible choices of NN can be written as ab\frac{a}{b}, where aa and bb are relatively prime positive integers. Compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
Let N be a positive integer. Brothers Michael and Kylo each select a positive integer less than or equal to N, independently and uniformly at random. Let p_(N) denote the probability that the product of these two integers has a units digit of 0. The maximum possible value of p_(N) over all possible choices of N can be written as (a)/(b), where a and b are relatively prime positive integers. Compute 100a+b.
Original LaTeX notation
Let $N$ be a positive integer. Brothers Michael and Kylo each select a positive integer less than or equal to $N$, independently and uniformly at random. Let $p_{N}$ denote the probability that the product of these two integers has a units digit of 0. The maximum possible value of $p_{N}$ over all possible choices of $N$ can be written as $\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100 a+b$.

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Source and history

task_id
7ef73575-0ae6-5bcf-bba4-d956555fe60b
task_key
test--7ef73575-0ae6-5bcf-bba4-d956555fe60b
task_revision_id
1
config / split
/ test

Official source

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