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Omni-MATH / Let X be the collection of all functions f:{0,1,…,2016}→{0,1,…,2016}. Compute the number of functions f∈X such that …

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problem

Let XX be the collection of all functions f:{0,1,…,2016}→{0,1,…,2016}f:\{0,1, \ldots, 2016\} \rightarrow\{0,1, \ldots, 2016\}. Compute the number of functions f∈Xf \in X such that maxg∈X(min0≤i≤2016(max(f(i),g(i)))−max0≤i≤2016(min(f(i),g(i))))=2015\max _{g \in X}\left(\min _{0 \leq i \leq 2016}(\max (f(i), g(i)))-\max _{0 \leq i \leq 2016}(\min (f(i), g(i)))\right)=2015
Plain-text mathematical notation (without MathML)
Let X be the collection of all functions f:{0,1,…,2016}→{0,1,…,2016}. Compute the number of functions f∈X such that max_(g∈X)(min_(0≤i≤2016)(max(f(i),g(i)))−max_(0≤i≤2016)(min(f(i),g(i))))=2015
Original LaTeX notation
Let $X$ be the collection of all functions $f:\{0,1, \ldots, 2016\} \rightarrow\{0,1, \ldots, 2016\}$. Compute the number of functions $f \in X$ such that $$\max _{g \in X}\left(\min _{0 \leq i \leq 2016}(\max (f(i), g(i)))-\max _{0 \leq i \leq 2016}(\min (f(i), g(i)))\right)=2015$$

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Source and history

task_id
d7a51d9b-b329-5a3c-bdb2-35bd70ede549
task_key
test--d7a51d9b-b329-5a3c-bdb2-35bd70ede549
task_revision_id
1
config / split
/ test

Official source

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