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Update informal/putnam.json
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Co-authored-by: Eric Wieser <[email protected]>
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elkhrt and eric-wieser authored Oct 7, 2024
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{
"problem_name": "putnam_2019_b6",
"informal_statement": "Let \\( \\mathbb{Z}^n \\) be the integer lattice in \\( \\mathbb{R}^n \\). Two points in \\( \\mathbb{Z}^n \\) are called neighbors if they differ by exactly 1 in one coordinate and are equal in all other coordinates. For which integers \\( n \\geq 1 \\) does there exist a set of points \\( S \\subset \\mathbb{Z}^n \\) satisfying the following two conditions? \\begin{enumerate} \\item If \\( p \\) is in \\( S \\), then none of the neighbors of \\( p \\) is in \\( S \\). \\item If \\( p \\in \\mathbb{Z}^n \\) is not in \\( S \\), then exactly one of the neighbors of \\( p \\) is in \\( S \\). \\end{enumerate}",
"informal_solution": "Show that the statement is true for every n \geq 1",
"informal_solution": "Show that the statement is true for every \\(n \\geq 1\\)",
"tags": [
"algebra"
]
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