+0  
 
+2
69
8
avatar+429 

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+429 
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.

 

 

coolcoolcool

 Jan 13, 2019
 #2
avatar+4033 
+2

there are 6 axes of reflection not 2

Rom  Jan 13, 2019
 #3
avatar+429 
0

that was what the answer was though... 420

 Jan 13, 2019
 #5
avatar+97599 
+1

The ansswer was wrong then.

Melody  Jan 13, 2019
 #4
avatar+97599 
+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.

 Jan 13, 2019
 #6
avatar+429 
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+4033 
+2

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+429 
0

oh ok

 Jan 15, 2019

15 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.