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Omni-MATH / A lattice point in the plane is a point of the form (n,m), where n and m are integers. Consider a set S of lattice points. We construct the transform of S, denoted by S^{prime}, by…

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problem

A lattice point in the plane is a point of the form (n,m)(n, m), where nn and mm are integers. Consider a set SS of lattice points. We construct the transform of SS, denoted by $S^{\prime}$, by the following rule: the pair (n,m)(n, m) is in $S^{\prime}$ if and only if any of (n,m−1),(n,m+1),(n−1,m)(n, m-1),(n, m+1),(n-1, m), (n+1,m)(n+1, m), and (n,m)(n, m) is in SS. How many elements are in the set obtained by successively transforming {(0,0)}14\{(0,0)\} 14 times?
Plain-text mathematical notation (without MathML)
A lattice point in the plane is a point of the form (n,m), where n and m are integers. Consider a set S of lattice points. We construct the transform of S, denoted by $S^{\prime}$, by the following rule: the pair (n,m) is in $S^{\prime}$ if and only if any of (n,m−1),(n,m+1),(n−1,m), (n+1,m), and (n,m) is in S. How many elements are in the set obtained by successively transforming {(0,0)}14 times?
Original LaTeX notation
A lattice point in the plane is a point of the form $(n, m)$, where $n$ and $m$ are integers. Consider a set $S$ of lattice points. We construct the transform of $S$, denoted by $S^{\prime}$, by the following rule: the pair $(n, m)$ is in $S^{\prime}$ if and only if any of $(n, m-1),(n, m+1),(n-1, m)$, $(n+1, m)$, and $(n, m)$ is in $S$. How many elements are in the set obtained by successively transforming $\{(0,0)\} 14$ times?

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task_id
d257fe69-d190-594e-a7ec-25b5a371ecde
task_key
test--d257fe69-d190-594e-a7ec-25b5a371ecde
task_revision_id
1
config / split
/ test

Official source

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