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The Number Rotation Puzzle (NRP) is a combination puzzle in which the goal isto rearrange a scrambled rectangular grid of numbers back into order via movesthat consist of rotating square blocks of numbers of fixed size. Over allpossible boards and rotating block sizes, we find all solvable initialconfigurations and provide algorithms to solve such configurations. Forsufficiently large board and rotating block sizes, solvability conditionsdepend only on parity restrictions, with special additional conditions forsmaller sizes. One special case leads to a novel construction of the exoticouter automorphism on $S_6$.

Solution to the Number Rotation Puzzle