by Isabel Harris
It is possible to have a set of 19 dice for a four player game, as shown in Figure 3. For clarity, the winning relationships for only one die, the median die, are shown. The red arrows denote that the median die beats the specified dice. The relationships among the remaining dice can be found by rotating the pattern of wins from the median die.
Because each row increases by 7(n-1), where n is the row number, we know every number in a certain row automatically beats all numbers in the preceding row or rows. Thus, we can focus on which and how many of the diagonal squares are won by each die. In the example in Figure 6, Die 1 wins the last square on the diagonal and Die 2 wins the other two squares on the diagonal. Therefore, Die 2 beats Die 1. This idea holds as we create larger dice sets for more players and makes for an easy check for winning die.
Disclaimer: The views and opinions in this work are those of the author and do not necessarily reflect the views of Auburn University.