+289 How many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same? (In other words, two arrangements are considered the same if I can rotate and/or reflect one arrangement to get the other. Assume that each square gets exactly one bead.) How many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same? (In other words, two arrangements are considered the same if I can rotate and/or reflect one arrangement to get the other. Assume that each square gets exactly one bead.)
Because of the rotation, you can fix one element and place all the others around it. This gives you a total of 90 possible arrangements.
+9673 I wrote a C++ program to simulate the situation.
EDIT: This part was originally the code, but the website removes angle brackets automatically, so I resorted to pastebin for the code.
Code: https://pastebin.com/gRWpfdam
Running the program results in: Number of ways is 180
