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Omni-MATH / Let n≥3 be a fixed integer. There are m≥n+1 beads on a circular necklace. You wish to paint the beads using n colors, such that among any n+1 consecutive beads every color appears …

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problem

Let n≥3n\ge 3 be a fixed integer. There are m≥n+1m\ge n+1 beads on a circular necklace. You wish to paint the beads using nn colors, such that among any n+1n+1 consecutive beads every color appears at least once. Find the largest value of mm for which this task is $\emph{not}$ possible. [i]Carl Schildkraut, USA[/i]
Plain-text mathematical notation (without MathML)
Let n≥3 be a fixed integer. There are m≥n+1 beads on a circular necklace. You wish to paint the beads using n colors, such that among any n+1 consecutive beads every color appears at least once. Find the largest value of m for which this task is $\emph{not}$ possible.

[i]Carl Schildkraut, USA[/i]
Original LaTeX notation
Let $n\ge 3$ be a fixed integer. There are $m\ge n+1$ beads on a circular necklace. You wish to paint the beads using $n$ colors, such that among any $n+1$ consecutive beads every color appears at least once. Find the largest value of $m$ for which this task is $\emph{not}$ possible.

[i]Carl Schildkraut, USA[/i]

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Source and history

task_id
c395ab72-8ab7-5264-824d-c9c987065b1d
task_key
test--c395ab72-8ab7-5264-824d-c9c987065b1d
task_revision_id
1
config / split
/ test

Official source

initial import