+0

# the answer is NOT 90

+2
79
4
+258

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.)

Apr 17, 2022

#1
+9457
+2

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

Apr 17, 2022
#2
+117494
0

Hi Max, it is great to see you here again !

Melody  Apr 18, 2022
#3
+117494
+1

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

Apr 18, 2022
edited by Melody  Apr 18, 2022
#4
+117494
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Glowlife,  if you are given an answer, maybe from your teacher, then please show us  (with the logic behind it if possible).

Melody  Apr 18, 2022