_AHA! Puzzle This By Michael H. Pryor

MAKE’s favorite puzzles. (When you’re ready to check your answers, visit makezine.com/09/aha.)

A Matter of Degree
What is the angle
between the minute
hand and the hour hand
at 3: 15 on an analog
clock? (Hint: It’s not 0.)
How often does the
minute hand pass
the hour hand on an
analog clock?

Reptilian Repetition At one point, a tropical island’s population of chameleons was divided as follows:

13 red chameleons 15 green chameleons 17 blue chameleons

Each time two different-colored chameleons would meet, they would change their color to the third one. For example, if green meets red, they both change their color to blue. Is it ever possible for all chameleons to become the same color? Why or why not?

Illustrations by Roy Doty

100 Lockers You have 100 lockers in a high school hallway that are all initially closed. You walk down the hallway 100 times starting at the first locker each time. The first time down the hallway, you go to every locker, and if it is open you close it; if it is closed, you open it. The second time you walk down the hallway, you only visit every second locker (lockers #2, #4, #6, etc), reversing the state of each locker you visit. The third time through, you visit every third locker (lockers #3, #6, #9, etc). You continue this until your 100th pass down the hallway when you only visit locker #100. When you are finished, which lockers are open and which are closed?

Michael Pryor is the co-founder and president of Fog Creek Software. He runs a technical interview site at techinterview.org.

Make: 189