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Omni-MATH / In a sports league, each team uses a set of at most t signature colors. A set S of teams is[i] color-identifiable[/i] if one can assign each team in S one of their signature colors…

Problem

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problem

In a sports league, each team uses a set of at most

t

signature colors. A set

S

of teams is[i] color-identifiable[/i] if one can assign each team in

S

one of their signature colors, such that no team in

S

is assigned any signature color of a different team in

S

. For all positive integers

n

and

t

, determine the maximum integer

g(n, t)

such that: In any sports league with exactly

n

distinct colors present over all teams, one can always find a color-identifiable set of size at least

g(n, t)

Plain-text mathematical notation (without MathML)

In a sports league, each team uses a set of at most t signature colors. A set S of teams is[i] color-identifiable[/i] if one can assign each team in S one of their signature colors, such that no team in S is assigned any signature color of a different team in S.

For all positive integers n and t, determine the maximum integer g(n,t) such that: In any sports league with exactly n distinct colors present over all teams, one can always find a color-identifiable set of size at least g(n,t).

Original LaTeX notation

In a sports league, each team uses a set of at most $t$ signature colors. A set $S$ of teams is[i] color-identifiable[/i] if one can assign each team in $S$ one of their signature colors, such that no team in $S$ is assigned any signature color of a different team in $S$.

For all positive integers $n$ and $t$, determine the maximum integer $g(n, t)$ such that: In any sports league with exactly $n$ distinct colors present over all teams, one can always find a color-identifiable set of size at least $g(n, t)$.

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task_id: eee4a97c-028d-53ef-b58a-0b147c551518
task_key: test--eee4a97c-028d-53ef-b58a-0b147c551518
task_revision_id: 4
config / split: / test

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