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Omni-MATH / Consider the set of 5-tuples of positive integers at most 5. We say the tuple…

Problem

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problem

Consider the set of 5-tuples of positive integers at most 5. We say the tuple (a1,a2,a3,a4,a5)\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right) is perfect if for any distinct indices i,j,ki, j, k, the three numbers ai,aj,aka_{i}, a_{j}, a_{k} do not form an arithmetic progression (in any order). Find the number of perfect 5-tuples.
Plain-text mathematical notation (without MathML)
Consider the set of 5-tuples of positive integers at most 5. We say the tuple (a₁,a₂,a₃,a₄,a₅) is perfect if for any distinct indices i,j,k, the three numbers a_(i),a_(j),a_(k) do not form an arithmetic progression (in any order). Find the number of perfect 5-tuples.
Original LaTeX notation
Consider the set of 5-tuples of positive integers at most 5. We say the tuple $\left(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right)$ is perfect if for any distinct indices $i, j, k$, the three numbers $a_{i}, a_{j}, a_{k}$ do not form an arithmetic progression (in any order). Find the number of perfect 5-tuples.

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Source and history

task_id
5ec7a391-839e-5f3b-9457-cde68b089676
task_key
test--5ec7a391-839e-5f3b-9457-cde68b089676
task_revision_id
1
config / split
/ test

Official source

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