The Prisoner's Dilemma

  • 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

  • D. S_D8

    PMP 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…

    Posted: 2023-11-19 21:09:52   Solutions will be accepted through

  • D. S_D7

    We received a solution from William Keehn and a partial solution from Jesse Waite of Fort Leavenworth. Both submitters realized that one straightforward way to control the numbers of sides of the cross-sections is to tip back the top-right vertex of the tetrahedron in the figure associated with the problem, straight toward its leftmost horizontal…

    Posted: 2023-11-19 19:31:00   Solutions will be accepted through

  • D13. The Experbola

    The Experbola

    In Dilemma 8, we investigated a curve similar to an ellipse, but changing addition to multiplication in its definition. This time, PMP participant William Keehn proposes a similar exploration related to the hyperbola, another conic section, which can be thought of as all of the points ( x , y ) in the plane where…

    Posted: 2023-05-01 13:40:34

  • D. S_D4

    As submitter Jesse Waite noted, a good first step in attacking one of these sequences is to write out (in symbols) the rule defining it, known as its recurrence relation. For example, if we denote the first series connected with addition by c 0 , c 1 , c 2 , … , its recurrence…

    Posted: 2022-07-02 12:46:47   Solutions will be accepted through

Contributor: Keehn_W