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D. S_D23
Posted: 2025-05-12 01:19:44 Solutions will be accepted throughOne elegant way to find an acceptable numbering is to assign every edge a different prime number, and then label each vertex by the product of the prime numbers assigned to all of the edges leaving it. Whatever primes you choose, that labeling satisfies all of the desired properties. However, it doesn’t in general produce…
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D. S_D19
Posted: 2024-09-30 20:44:44 Solutions will be accepted throughYael Eisenberg (Cornell University), the Eagle Problem Solvers of Georgia Southern, Chris Bistryski (PMP), and Randy Schwartz (Schoolcraft College) wrote in about this one. The condition that you were neither first nor last means that you had exactly two neighbors in line. Since presumably the order of the line was random, choosing your two neighbors…
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D. S_D16
Posted: 2024-09-30 19:56:13 Solutions will be accepted throughWe heard from Chris Bistryski (PMP), Robert Noll (PMP), and Randy Schwartz (Schoolcraft College) on this one. The first construction below, of a single coin that works in six flips, was submitted by Chris. Note that it is just the number of heads and tails in a given sequence that determines the probability of that…
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D. S_D12
Posted: 2023-11-21 12:02:15 Solutions will be accepted throughWe received solutions from Chris Bistryski, William Keehn, Blazej Kot, and Robert Noll, all PMP participants. All of the solutions proceeded algebraically by assigning a variable to the value of one of Mathophila’s numbers, which determines the others since her five numbers are all consecutive. But Robert pointed out that the algebra works out most…
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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…