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# Repost (last one, the image failed)

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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?

Jan 12, 2019

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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.

Jan 13, 2019
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there are 6 axes of reflection not 2

Rom  Jan 13, 2019
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that was what the answer was though... 420

Jan 13, 2019
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The ansswer was wrong then.

Melody  Jan 13, 2019
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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.

Jan 13, 2019
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i use a website called art of problem solving, in their resource called alcumus they said it was 420... im really confused i dont know

Jan 14, 2019
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What might be going on is that 3 of the axes of symmetry do not intersect any of the dots.

The website in question might not consider these axes of symmetry.

140 x 3 = 420

Rom  Jan 14, 2019
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oh ok

Jan 15, 2019