BMAD 65 Posted October 18, 2013 Report Share Posted October 18, 2013 Joining every vertex of a convex pentagon to every other vertex forms three nested figures: the original outer pentagon an inner pentagon a five-pointed star between them Suppose the perimeters of these three figures are all primes; show that the three primes’ sum is at least 20. Quote Link to post Share on other sites

0 phil1882 13 Posted October 19, 2013 Report Share Posted October 19, 2013 no clue about this one. seems to me the lowest prime number the outside could be is 11, with the blue diamond being 7 and the black pentagon being 3. but how to prove that is beyond me. Quote Link to post Share on other sites

0 jordge 2 Posted October 20, 2013 Report Share Posted October 20, 2013 no clue about this one. seems to me the lowest prime number the outside could be is 11, with the blue diamond being 7 and the black pentagon being 3. but how to prove that is beyond me. When you said the blue diamond, did you mean the blue star? If so, it would have a larger perimeter than the red pentagon. But that is all I can determine. Quote Link to post Share on other sites

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