What’s the most interesting mathematical puzzle you’ve solved?

Question: What's the most interesting mathematical puzzle you've solved?
- Keywords:
  interesting,
  mathematics,
  puzzle
Asked by tanglewood12 to Nick on 12 Mar 2014.
- Nick Goldman answered on 12 Mar 2014:
  
  Oh, there’s been so many. Here’s one I did last night. Draw an equilateral triangle (all sides the same length, all angles 60 degrees). Now draw the biggest circle that will fit inside it, and the smallest circle that will fit outside it. What is the ratio of the radius of the big circle to the radius of the small circle?

Anna commented on 12 Mar 2014:

OMG! Is this what you do in your evenings? Love it!

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modandy commented on 12 Mar 2014:

Is it Phi?

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Question: What's the most interesting mathematical puzzle you've solved?