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**+2 **

Please refer to this programming solution from me: https://web2.0calc.com/questions/hlp_25#r2

MaxWong Apr 17, 2022

#3**+1 **

I think your answer is too big Max ://

If the beads were just in a circle, where just rotations are the same then the answer woud be 5! = 120

But there are less options than this because of the reflection aspect.

As far as reflection goes, these 3 are the same

So I am thinking tht the answer might be 120/3 = 40

Melody Apr 18, 2022