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Omni-MATH / The numbers a₁,a₂,…,a₁₀₀ are a permutation of the numbers 1,2,…,100. Let S₁=a₁, S₂=a₁+a₂,…,S₁₀₀=a₁+a₂+…+a₁₀₀. What maximum number of perfect squares can be among the numbers …

Problem

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problem

The numbers a1,a2,…,a100a_{1}, a_{2}, \ldots, a_{100} are a permutation of the numbers 1,2,…,1001,2, \ldots, 100. Let S1=a1S_{1}=a_{1}, S2=a1+a2,…,S100=a1+a2+…+a100S_{2}=a_{1}+a_{2}, \ldots, S_{100}=a_{1}+a_{2}+\ldots+a_{100}. What maximum number of perfect squares can be among the numbers S1,S2,…,S100S_{1}, S_{2}, \ldots, S_{100}?
Plain-text mathematical notation (without MathML)
The numbers a₁,a₂,…,a₁₀₀ are a permutation of the numbers 1,2,…,100. Let S₁=a₁, S₂=a₁+a₂,…,S₁₀₀=a₁+a₂+…+a₁₀₀. What maximum number of perfect squares can be among the numbers S₁,S₂,…,S₁₀₀?
Original LaTeX notation
The numbers $a_{1}, a_{2}, \ldots, a_{100}$ are a permutation of the numbers $1,2, \ldots, 100$. Let $S_{1}=a_{1}$, $S_{2}=a_{1}+a_{2}, \ldots, S_{100}=a_{1}+a_{2}+\ldots+a_{100}$. What maximum number of perfect squares can be among the numbers $S_{1}, S_{2}, \ldots, S_{100}$?

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Source and history

task_id
50714739-396e-5663-9fa2-39264a0eeb35
task_key
test--50714739-396e-5663-9fa2-39264a0eeb35
task_revision_id
1
config / split
/ test

Official source

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