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A regular pentagon is cut out of a flat piece of cardboard. The pentagon is then placed back into the pentagonal hole. How many ways can the pentagon be placed back into the hole, if the pentagon can be rotated and/or reflected?


I know that it can be reflected 5 ways... but I don't get how many times it can be rotated. I thought I would be either 20 or 25, but no. Can anybody help with this problem? Thanks!

 Feb 20, 2021
 #1
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A pentagon can be rotated 5 ways and still have it look the same. I hope this helps. I myself still am not sure of the solution yet.

 Feb 20, 2021
 #2
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Can anybody help with this problem?  

 

Is it legal to flip the pentagon over, so that the back side of the cardboard is now facing up?  

 Feb 20, 2021
 #3
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I think it might be, in which case I think there might be 50 solutions

Guest Feb 20, 2021
 #4
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Five ways with the face up     five more ways with the face reflected to the back ....    10 ways

 Feb 20, 2021
 #5
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I'm not sure whether there's one line of symmetry or 5...

Guest Feb 20, 2021
 #6
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Yes, thanks! The answer was 10 smiley

Guest Feb 20, 2021

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