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_D21

    Assign a red light a value of 0, a green light a value of 1, and a yellow light a value of 2. Now consider the sum of the values of all of the lights in arithmetic modulo 3. Under this assignment, pushing any button increases the value of exactly three lights by 1 mod…

    Posted: 2025-05-12 01:00:32   Solutions will be accepted through

  • D. S_D20

    Christopher West (PMP) and the Georgia Southern Eagle Problem Solvers got this one. The answer is that E can be any point at all on C D , because no matter what points E and F are chosen, the purple and pink areas are equal. To see this, note that by the usual area formula…

    Posted: 2024-09-30 20:51:11   Solutions will be accepted through

  • D. S_D18

    Anthony Batiste and the Georgia Southern University problem group solved this dilemma. One can generate the solutions by assigning variables to each of the squares in turn from left to right, noting that every touching pair must be equal, and then finding integer solutions where the two required totals are equal to five. That analysis…

    Posted: 2024-09-30 20:32:44   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_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

Contributor: Eagle_PS