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 primesâ€™ sum is at least 20. 0 Share this post Link to post Share on other sites

0 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. 0 Share this post Link to post Share on other sites

0 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. 0 Share this post Link to post Share on other sites

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