Category Archives: Puzzles and Problems

Ant Problem

This is one of Alex Bellos’s Monday Puzzles in the Guardian. I basically found the same solution as Bellos and his commenters, but wrote it up with what I thought were more explanatory graphics. The idea is that there is a bunch of ants on a stick who all walk a the same speed of 1 centimeter per second. When an ant runs into another ant, they both turn around and go the opposite direction. “So here is the puzzle: Which ant is the last to fall off the stick? And how long will it be before he or she does fall off?”  See the Ant Problem.

 

Power of 2 Problem

Virtually the very first “math” problem I got interested in involved a 7th grade homework problem in 2005 that a colleague at work said her son had been given. I ended up commenting and helping on a number of further problems, which gave me some insight into the state of current public school teaching in mathematics. It was both encouraging and discouraging at the same time. I will join the math education commentary at a later date.

The problem was not that bad: What is the largest power of 2 that divides 800! without a remainder? (where “!” means “factorial”, for example, 5! = 5 x 4 x 3 x 2 x 1). I solved it in my usual pedestrian way. I showed it to a friend of mine (an algebraist!) and he of course had a nifty approach. He showed it to a colleague of his at NSF (a physicist) and he had the niftiest solution of all! (Most humbling.) See the Power of 2 Problem.