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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
 #1
avatar+532 
+1

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.

 

 

coolcoolcool

 Jan 13, 2019
 #2
avatar+6251 
+1

there are 6 axes of reflection not 2

Rom  Jan 13, 2019
 #3
avatar+532 
+1

that was what the answer was though... 420

 Jan 13, 2019
 #5
avatar+118667 
0

The ansswer was wrong then.

Melody  Jan 13, 2019
 #4
avatar+118667 
0

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
 #6
avatar+532 
0

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
 #7
avatar+6251 
+1

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
 #8
avatar+532 
0

oh ok

 Jan 15, 2019

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