Combinatorics · Counting · Symmetry · Permutations
Every cell of a \(3 \times 3\) board is to be painted in one of \(9\) colors so that all \(9\) colors are used. How many differently colored boards can be made? (Two boards are colored differently if they cannot be brought to coincide by a motion in the plane.)
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Serbian Municipal Competition 1995, high school grade I, problem 4. Organized by the Mathematical Society of Serbia (DMS).