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Omni-MATH / Yann writes down the first n consecutive positive integers, 1,2,3,4,…,n−1,n. He removes four different integers p,q,r,s from the list. At least three of p,q,r,s are consecutive and…

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problem

Yann writes down the first nn consecutive positive integers, 1,2,3,4,…,n−1,n1,2,3,4, \ldots, n-1, n. He removes four different integers p,q,r,sp, q, r, s from the list. At least three of p,q,r,sp, q, r, s are consecutive and 100<p<q<r<s100<p<q<r<s. The average of the integers remaining in the list is 89.5625. What is the number of possible values of ss?
Plain-text mathematical notation (without MathML)
Yann writes down the first n consecutive positive integers, 1,2,3,4,…,n−1,n. He removes four different integers p,q,r,s from the list. At least three of p,q,r,s are consecutive and 100<p<q<r<s. The average of the integers remaining in the list is 89.5625. What is the number of possible values of s?
Original LaTeX notation
Yann writes down the first $n$ consecutive positive integers, $1,2,3,4, \ldots, n-1, n$. He removes four different integers $p, q, r, s$ from the list. At least three of $p, q, r, s$ are consecutive and $100<p<q<r<s$. The average of the integers remaining in the list is 89.5625. What is the number of possible values of $s$?

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task_id
e8c6567a-e101-5172-b9b8-5bf1d0710ba4
task_key
test--e8c6567a-e101-5172-b9b8-5bf1d0710ba4
task_revision_id
1
config / split
/ test

Official source

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