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.)

Glowlife Apr 17, 2022

#1**0 **

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.

Guest Apr 17, 2022

#2**+1 **

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**

MaxWong Apr 17, 2022