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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
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Scrambling a “Connections” grid
Yes, here is one solution for the 4-by-4 case found by a computer search. Each array is obtained from the previous one by applying the permutation (0 1 2 3 4)(5 6 7 8 9)(10 11 12 13 14) to the entries …