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D. S_D9
Posted: 2023-11-20 12:13:29 Solutions will be accepted throughFor convenience, since segment A C is divided into four equal parts, we introduce coordinates scaled so that A C = 4 . We place the origin at the center of the (semi)ellipse, which is to say the midpoint between the foci F and G . Thus the equation of the ellipse will have the…
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D. S_D8
Posted: 2023-11-19 21:09:52 Solutions will be accepted throughPMP participants Chris Bistryski of Monroe, WA, William Jones of FCI Loretto, William Keehn, and Jesse Waite submitted solutions to this problem. As Mr. Keehn pointed out, it’s smoothest to work with polar coordinates; see Figure 2 for an illustration of the coordinates ( r , θ ) of a general point M on the…
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D. S_D6
Posted: 2023-11-19 15:45:55 Solutions will be accepted throughWe received solutions to this Dilemma from Matthew Helmer (Pacific Lutheran University), William Jones (PMP), and Jesse Waite (PMP), and partial solutions from Christopher Havens (PMP Founder) and Sonny Kim (PMP). As Jesse pointed out, the rectangles look like dominoes (length twice the width), but since we want the exact answer, we’d better not rely…
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D. S_D5
Posted: 2023-11-17 09:30:37 Solutions will be accepted throughWe received solutions from PMP participants William Jones and Sonny Kim. Imagine your bets on Tee Bone, New York Strip, and Rib Eye are t , n , and r dollars, respectively, where of course t + n + r = 94 . Then, if Tee Bone, New York Strip, or Rib Eye wins, you…
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D. S_D2
Posted: 2022-07-01 19:40:15 Solutions will be accepted throughAdmittedly, it looks bleak for the people in this situation. If each person involved simply checks half of the boxes at random, there’s only a 50 / 50 chance of finding the right number, and so only a 1 in 2100 chance of everyone finding their number. That’s a truly minuscule chance, because 2100 is…