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_D22

    Consider the case n = 1 in which you precisely fit one cookie in a 2×2 square, leaving 4 − π square units of cookie dough, which are “wasted” in that you cannot make any further cookies. This case shows two things: (a) you must always waste at least 4 − π square units of…

    Posted: 2025-05-12 01:08:38   Solutions will be accepted through

  • D. S_D17

    The proposer Akiva Weinberger provided a twist on the classic “proof on the back of a napkin,” namely, a “solution using a napkin”: In case it’s not quite clear how to rearrange the pieces, here are the “before” and “after” diagrams with the corresponding pieces numbered. If you can find a way to do it…

    Posted: 2025-05-12 00:48:14   Solutions will be accepted through

  • D. S_D13

    The Prisoner’s Dilemma received submissions from three PMP participants: a full one from Christopher West, a nearly complete solution from Blazej Kot, and one from Andrew Trentacoste II. The Eagle Problem Solvers of Georgia Southern University also submitted a very thorough solution. Every complete solution received relied on methods of calculus, so we follow such…

    Posted: 2024-09-30 18:24:55   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

Contributor: Kot_B