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Omni-MATH / How many ways are there to choose 2010 functions f₁,…,f₂₀₁₀ from …f₂₀₁₀∘f₂₀₀₉∘⋯∘f₁ is constant? Note: a function g is constant if g(a)=g(b) for all a,b in the domain of g.

Problem

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problem

How many ways are there to choose 2010 functions f1,…,f2010f_{1}, \ldots, f_{2010} from \{0,1\} to \{0,1\} such that f2010∘f2009∘⋯∘f1f_{2010} \circ f_{2009} \circ \cdots \circ f_{1} is constant? Note: a function gg is constant if g(a)=g(b)g(a)=g(b) for all a,ba, b in the domain of gg.
Plain-text mathematical notation (without MathML)
How many ways are there to choose 2010 functions f₁,…,f₂₀₁₀ from \{0,1\} to \{0,1\} such that f₂₀₁₀∘f₂₀₀₉∘⋯∘f₁ is constant? Note: a function g is constant if g(a)=g(b) for all a,b in the domain of g.
Original LaTeX notation
How many ways are there to choose 2010 functions $f_{1}, \ldots, f_{2010}$ from \{0,1\} to \{0,1\} such that $f_{2010} \circ f_{2009} \circ \cdots \circ f_{1}$ is constant? Note: a function $g$ is constant if $g(a)=g(b)$ for all $a, b$ in the domain of $g$.

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Source and history

task_id
cbb5063d-0dc8-5f39-b8c9-41e41f31ed30
task_key
test--cbb5063d-0dc8-5f39-b8c9-41e41f31ed30
task_revision_id
1
config / split
/ test

Official source

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