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Omni-MATH / Each lattice point with nonnegative coordinates is labeled with a nonnegative…

Problem

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problem

Each lattice point with nonnegative coordinates is labeled with a nonnegative integer in such a way that the point (0,0)(0,0) is labeled by 0 , and for every x,y≥0x, y \geq 0, the set of numbers labeled on the points (x,y),(x,y+1)(x, y),(x, y+1), and (x+1,y)(x+1, y) is \{n, n+1, n+2\} for some nonnegative integer nn. Determine, with proof, all possible labels for the point (2000,2024)(2000,2024).
Plain-text mathematical notation (without MathML)
Each lattice point with nonnegative coordinates is labeled with a nonnegative integer in such a way that the point (0,0) is labeled by 0 , and for every x,y≥0, the set of numbers labeled on the points (x,y),(x,y+1), and (x+1,y) is \{n, n+1, n+2\} for some nonnegative integer n. Determine, with proof, all possible labels for the point (2000,2024).
Original LaTeX notation
Each lattice point with nonnegative coordinates is labeled with a nonnegative integer in such a way that the point $(0,0)$ is labeled by 0 , and for every $x, y \geq 0$, the set of numbers labeled on the points $(x, y),(x, y+1)$, and $(x+1, y)$ is \{n, n+1, n+2\} for some nonnegative integer $n$. Determine, with proof, all possible labels for the point $(2000,2024)$.

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Source and history

task_id
606d5695-aedf-53e3-92df-dc589a4dd017
task_key
test--606d5695-aedf-53e3-92df-dc589a4dd017
task_revision_id
1
config / split
/ test

Official source

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