numberlink
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How strict do we want to be?
Maybe the "1 neighbor for endpoints, 2 for midpoints" rule is too harsh. Janko.at has an interesting version of Numberlink called Arukone^3, which provides the rule "A single line must not cover an area if size 2x2 or larger." This more pragmatic requirement lets us solve puzzles like http://www.janko.at/Raetsel/Arukone/190.a.htm (which has a
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thing going on in the lower left corner. The change wouldn't affect performance in any way, since this is enforced only by the final validator.