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Omni-MATH / Find all functions fcolon mathbb{Z}^2 to [0, 1] such that for any integers x and y, f(x,y)=(f(x−1,y)+f(x,y−1))/(2).

Problem

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problem

Find all functions $f\colon \mathbb{Z}^2 \to [0, 1]$ such that for any integers

x

and

y

f(x, y) = \frac{f(x - 1, y) + f(x, y - 1)}{2}.

Plain-text mathematical notation (without MathML)

Find all functions $f\colon \mathbb{Z}^2 \to [0, 1]$ such that for any integers x and y,
f(x,y)=(f(x−1,y)+f(x,y−1))/(2).

Original LaTeX notation

Find all functions $f\colon \mathbb{Z}^2 \to [0, 1]$ such that for any integers $x$ and $y$,
\[f(x, y) = \frac{f(x - 1, y) + f(x, y - 1)}{2}.\]

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task_id: d8a2764a-0782-58a3-8a81-eaef0f7e434d
task_key: test--d8a2764a-0782-58a3-8a81-eaef0f7e434d
task_revision_id: 4
config / split: / test

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