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# hlp

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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.) 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

### 2+0 Answers

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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
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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.

Running the program results in: Number of ways is 180

Apr 17, 2022
edited by MaxWong  Apr 17, 2022