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Smallest completely fillable square

Besides the 1 by 1 square, which is trivial, what is the smallest square that can be filled completely? It turns out, it is the 5 by 5 square and there are 12400 different ways of filling it. The 4 by 5 grid can also be filled completely; in 144 unique ways. See the following examples. Continue reading →

Fastest way to get stuck

The goal of this puzzle is to fill the 10 by 10 grid with numbers from 1 to 100 without getting stuck along the way. Let's see how fast one can get into trouble. Suprisingly, one can get stuck in just 6 moves. Up to symmetry, translation and rotation there are 3 unique ways of getting stuck in 6 moves. Continue reading →

Warnsdorff's rule

Warnsdorff's rule is a heuristic for finding a knight's tour. The knight is moved so that it always proceeds to the square from which the knight will have the fewest onward moves. When calculating the number of onward moves for each candidate square, we do not count moves that revisit any square already visited. Continue reading →