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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
7
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The "sensitivity" of 2-colorings of the d-dimensional integer lattice
Here's another problem that is equivalent to this one (see http://www.cs.huji.ac.il/~nati/PAPERS/gotsman_equivalence.pdf):
Consider a 2-coloring of the vertices of the n-dimensional hypercube. We sa …