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Omni-MATH / Each of eight boxes contains six balls. Each ball has been colored with one of…

Problem

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problem

Each of eight boxes contains six balls. Each ball has been colored with one of nn colors, such that no two balls in the same box are the same color, and no two colors occur together in more than one box. Determine, with justification, the smallest integer nn for which this is possible.
Plain-text mathematical notation (without MathML)
Each of eight boxes contains six balls. Each ball has been colored with one of n colors, such that no two balls in the same box are the same color, and no two colors occur together in more than one box. Determine, with justification, the smallest integer n for which this is possible.
Original LaTeX notation
Each of eight boxes contains six balls. Each ball has been colored with one of $n$ colors, such that no two balls in the same box are the same color, and no two colors occur together in more than one box. Determine, with justification, the smallest integer $n$ for which this is possible.

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Source and history

task_id
620ba07b-5cd6-5243-aad1-0531940f8b0f
task_key
test--620ba07b-5cd6-5243-aad1-0531940f8b0f
task_revision_id
1
config / split
/ test

Official source

initial import