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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_D15
Posted: 2024-09-30 19:24:52 Solutions will be accepted throughRobert Noll (PMP), Randy Schwartz (Schoolcraft College), and the Eagle Problem Solvers of Georgia Southern University submitted solutions. The key observation is that if the elliptical track ever lies outside of the circle of radius two centered at (1, 0), then it will have to intersect that circle again for some x value greater than…