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

 Apr 17, 2022
 #2
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Hi Max, it is great to see you here again !

Melody  Apr 18, 2022
 #3
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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

 Apr 18, 2022
edited by Melody  Apr 18, 2022
 #4
avatar+118117 
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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

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