In how many ways can seven beads of distinct colors be put on the hexagonal grid shown, if reflections and rotations of an arrangement are considered equivalent?

asdf335 Jan 12, 2019

#1**0 **

i guess i will answer this myself... there are 7 choices for the inner dot, and you can draw a circle around the other six, so the number of ways for those is 6!/6 for rotations. so it is 7*120=840, but there are reflections, so it is 840/2=420.

asdf335 Jan 13, 2019

#4**+1 **

I answered this one a short time ago.

Lets see.

7*5! = 840 that takes care of rotation

There are 6 axes of symmetry so I think that should be divided by 6

7*5!/6 = 140

420 is definitely NOT correct.

140 might be correct.

Melody Jan 13, 2019