**Puzzle 10:** A baseball owner prints 1-4 stars by his players' names on the program based on which quartile their batting average is in (4 stars being best), and 0 stars by the names of players whose batting average is undefined (0 official at-bats). The mapping from players (ordered by batting average, if any) to number of stars (standard ordering) is monotone.

**Puzzle JW1:** In this example, the *converse* of the monotone mapping condition can fail in two ways. What are they?

**Puzzle JW2:** Is the mapping still monotone if the players with undefined averages are lumped in with the 2-star players (i.e. given 2 stars instead of 0)?