The Aliens and Presidents Puzzle

This post is about a very tricky math puzzle, and really has very little to do with aliens or presidents. This puzzle made the rounds stumping people at Reed College in 2014, and was created by my friend Steve Silverman (who seems to have an unlimited supply of unique puzzles of his own design). All credit for cleverness and ingenuity goes to him. This post was written because there were several people who did not believe that this puzzle had a real, unique, solution or else that there was some wordplay involved rather than mathematics. The puzzle begins below:

There are aliens living in a nearby solar system, and they love to travel. They also eat humans. On some day after 1800 they realize that one of their journeys will take them past Earth, and so they decide to ‘check out the menu’ and determine whether it would be worthwhile to stop on Earth for lunch. Now some humans are edible, and the rest are inedible. The advance scouting party that the Aliens send to see whether a stop would be viable perform a complete, precise, and instant census. They discover that the chance that two humans selected at random would both be inedible is exactly 50%. They determine that the venture would be uneconomical, and left.

Question: On that day who was president of the United States?

Click here to see the solution.

I love this puzzle because it needs no advanced mathematics (anything beyond elementary probability and you’re probably on the wrong track), and yet continues to stump so many people…including some very skilled mathematicians. It also serves as a demonstration of the incredible power of mathematics to find solutions in situations that seem impossible; in this case by exploiting structure in the problem that carries more import than intuition would predict. “How the hell…?” is the normal reaction to this puzzle, and yet the solution exists and is accesible to the pioneering mind with only minimal training.