D. S_D18

Contributed by Anthony Batiste and Eagle Problem Solvers, Georgia Southern University and Georgia Southern University

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 has quite a few cases, so we won’t give it in detail here, because Ian has already provided the information that there are exactly three other solutions. Therefore, it suffices to simply show the solutions, which we do in Figure 11.

Figure 11: The three other arrangements with five pips at the end and five in the middle.

This problem originally appeared in the Prisoner’s Dilemma in the issue of the PMP Newsletter. Solutions will be accepted through .