AHA! Puzzle This By Michael H. Pryor
MAKE’s favorite puzzles. (When you’re ready to check your answers, visit makezine.com/06/aha.)
Your roommate challenges you to a game with the quarters from each of your sock drawers. Whoever wins the game gets to keep all the money. (Assume you each have an unlimited supply of quarters.)
You sit down at the perfectly round kitchen table and each person takes a turn, placing a quarter down anywhere on the table. No quarters can overlap and the entire quarter must rest on the table surface. The
first person that can’t put a quarter down on the table loses. You each have plenty of quarters and won’t run out during the game.
Your roommate wants to go first. But you think about it for a while and realize you would much rather go first because you’ve figured out a surefire method to win (without cheating). After some convincing, your roommate allows you to place the first quarter. Where do you place it, and what is your winning strategy?
In-Your-Head Math How many trailing zeroes are there in 100 factorial ( 100!)? ( 100 factorial is 100 * 99 * 98 * etc., down to 1.) For example, 5,030,499,400,000 has five trailing zeroes.
How many points are there on Earth where a person can walk one mile south, one mile east, and then one mile north and end up in the same spot they started in? To be precise, let’s assume the Earth is a solid smooth sphere, without oceans or mountains.
The North Pole is one such place where you can walk one mile south, one mile east, one mile north and end up where you started. But is there another starting point that works?
If you think you’ve figured it out, I’ll give you a hint. There is more than one point. In fact, there are more than two points.
Each morning I come into work and arrange two normal cubes on my desk to display the current day of the month. For example, on the 1st of the month, the cubes have a 0 and a 1 on them. On the 16th day of the month, one cube has a 1 and the other a 6. On the 31st day of the month, a 3 and a 1 appear on the front of the cubes. Each cube has six sides and one number painted on each side. What are the numbers painted on each cube?
Michael Pryor is the co-founder and president of Fog Creek Software. He runs a technical interview site at techinterview.org.
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