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Grouping, Partitions, and Coloring

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Explanations 1

Invariants are, typically, things that stay invariant (don't change) during a process. Here's an example. Here's another example, where there's not really a process, but we can …
By Victor Wang

Problems 1

Let SSS be the set of all lattice points (x,y)(x, y)(x,y) in the plane satisfying ∣x∣+∣y∣≤10|x|+|y|\le 10∣x∣+∣y∣≤10. Let P1,P2,…,P2013P_1,P_2,\ldots,P_{2013}P1,P2,…,P2013 be …