The Prisoner's Dilemma

  • D. S_D23

    One 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…

    Posted: 2025-05-12 01:19:44   Solutions will be accepted through

  • D. S_D16

    We 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…

    Posted: 2024-09-30 19:56:13   Solutions will be accepted through

  • D. S_D15

    Robert 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…

    Posted: 2024-09-30 19:24:52   Solutions will be accepted through

  • D. S_D14

    Marion Cohen (Drexel University), Matthew Helmer (Pacific Lutheran University), and Robert Noll (PMP) solved this before we published a correction to an earliermisprint (which substituted f ( x ) − f ( y ) in place of f ( x − y ) , subtly changing the problem although not the answer). Nick Rauh (Seattle…

    Posted: 2024-09-30 19:09:09   Solutions will be accepted through

  • D. S_D12

    We 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…

    Posted: 2023-11-21 12:02:15   Solutions will be accepted through

  • D. S_D11

    This problem received submissions from PMP participants William Keehn, Blazej Kot, and Robert Noll. All solutions proceeded roughly as so: Let s = B C be the side of the square. Since the rightmost white rectangle has area s 2 / 8 , its width is s / 8 , and so the length of…

    Posted: 2023-11-20 22:12:17   Solutions will be accepted through

  • D. S_D10

    The Prisoner’s Dilemma received solutions from PMP participants William Keehn and Robert Noll; we follow primarily the former. First show that the minimum number of moves to solve the usual Tower of Hanoi puzzle with n discs is H n = 2 n − 1 , by breaking the problem into shifting the top n…

    Posted: 2023-11-20 21:57:47   Solutions will be accepted through

Contributor: Noll_R