## 1000.55 – Novice Bagpipers

The Ohio Scottish Highland Games includes classes for beginning bagpipers. At the end of their day of practice, the novice pipers come out and stand in a circle on the grass in the town square. As a way of taking roll for the group, they then count off. You, let us suppose, are standing right behind a girl who calls out #16, and you notice that the boy directly across the circle from her is #47. How many are in the class?

## Solution

There are 31 class members in the half circle from #16 to #47, that is, starting with #17, going on to #18, and so on, up to and including #47. There must be another 31 pipers in the other half circle back from #46 to #16, including #16. Thus there are 62 members in the class altogether. Once they start playing their tunes you can hear them all over town. (Of course, if you were really standing there you could just let them finish counting off and then you'd know right away how many pipers there were.)