const uint numBits = 3*numPieces; const u64 lowBits = ((1ULL << numBits)-1); const u64 highBits = lowBits << numBits; const u64 allFours = 04040404040404

const uint numBits = 3*numPieces; const u64 lowBits = ((1ULL << numBits)-1); const u64 highBits = lowBits << numBits; const u64 allFours = 04040404040404040404; const u64 allTwos = 02020202020202020202; // Flip around horizontal axis flippedIndex = index ^ (allFours & lowBits); // Flip around vertical axis flippedIndex = index ^ (allTwos & lowBits); Is my fix for the first two, but, as you point out, they're significantly easier. The patterns are pretty neat, but I can't figure out how they result in any sort of rule for diagonal flipping.