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Paramount Polygon Poser (Posted on 2015-01-15) Difficulty: 3 of 5
Each interior angle of a regular R-gon is precisely 59/58 times that of each angle of a regular S-gon, where R ≥ S ≥ 3.

Find the largest possible value of S.

No Solution Yet Submitted by K Sengupta    
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solution | Comment 2 of 3 |
We have 180 * (R-2)/R = (59/58) * 180 * (S-2)/S.

A little algebra gives RS - 118R + 116S = 0
and the factoring (R+116)*(S-118) = -116*118 

It's clearer to get rid of the negative sign and write (R+116)*(118-S) = 116*118

It's obvious now that S=117 is the maximum, making R=116*118 - 116 = 13572.


  Posted by xdog on 2015-01-15 10:52:06
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