Question 19.48

18. When it snows in the winter, the local school district superintendent must decide by 5 A.M. whether to declare a snow day and cancel school. The 900 faculty and staff are now notified by a robocall broadcast, but formerly a binary “telephone tree” was used, in which the superintendent called two people and each person who received a call called two others. Suppose that each call takes exactly 1 minute.

  1. Draw the telephone tree of calls for, and determine how many calls take place in, the first 1 minute, 2 minutes, 3 minutes, 4 minutes, and 5 minutes.
  2. How many calls does it take to notify all the faculty and staff? How long does that take?

(This exercise was inspired by a puzzle at the website by Ron Knott.)