Chapter 8.2, Problem 49MS

Picking up the tab (H). Ed and Mike go out to lunch and decide to roll dice to determine who will pick up the tab. They each roll the same collection of dice. Ed’s roll shows all 5’s and 3’s, with a total on all the dice of 21. Mike’s roll show all 2’s and 6’s, with a total of 18. Mike loses, so he picks up the tab, but that’s not the point here. Suppose the number of 5’s in Ed’s roll was the same as the number of 2’s in Mike’s roll, and the number of 3’s in Ed’s roll was the same as the number of 6’s in Mike’s roll. How many dice were Ed and Mike rolling? And who ordered the raw broccoli?