Motion System Design

# Fun with Fundamentals: Problem 234

Problem 234 – Hat trick
Put on your thinking cap, for this riddle could make your head spin. For generations the Piacée family has run Chez Sneubé, a five star restaurant in Paris. Francis Piacée, the adventurer of the family and founder of the restaurant, spent most of his days sailing the world, collecting fine spices and exotic recipes with his trusty captain Rex LeSheape and expert chef Pierre Burnette.

An adventure, indeed, is what Monsieur Piacée and company encountered when sailing the South Pacific in 1721 in search of true Tahitian vanilla. Pirates lurked along the trade route, but the captain assured all aboard he had successfully maneuvered the dangerous waters many times. Nevertheless, skull and crossbone flags quickly circled the galleon.

The infamous pirate Jacques du Chagrin and his posse of outcast rogues took the three men to a nearby vacant island. Soon to join them was Aufael Auder, a suspected traitor among Jacques’ ranks. The four prisoners were buried in sand up to their necks, unable to move or even turn their heads.

Jacques had his crew erect a wall between the captain and the other three men. Francis faced the wall, and behind him was Pierre followed by Aufael. Jacques switched the men’s hats such that no one knew which hat was on his head.

The men knew only that there were two white hats and two black hats. Jacques demanded that one man tell him what color his hat was.

“If the man who chooses to speak is wrong, you all drown when the tide comes in,” Jacques threatened. “If he’s right, we’ll at least dig you up before we desert you,” he added with a wicked smirk. Luckily for the doomed motley crew, one of the men was able to give the correct answer. Which man was it?

This month’s problem was submitted by Knute Hancock, Kinnelon, N.J.

Solution to the March problem, 233: Parting painters