+0  
 
+2
85
2
avatar+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.) 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
avatar
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.

 Apr 17, 2022
 #2
avatar+9457 
+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

 Apr 17, 2022
edited by MaxWong  Apr 17, 2022

11 Online Users

avatar
avatar