Barge Problem: The Answer is not 42

While hitchhiking through the galaxy you and your friend, let’s call him Ford, find yourselves imprisoned by the Vogons, a grotesque alien species, on an unremarkable planet orbiting the distant star Betelgeuse. Your captors offer you the following opportunity at freedom. They tell you that Ford will be escorted into a separate room containing only a deck of (ordinary) cards and four bins labeled 1-4. Ford must then select any 5 cards from this deck. (Apparently Vogons have an affinity for cards.) After looking at the cards Ford will then give 1 card of his choice to the Vogon guard and place the remaining 4 cards face up in the bins so that each bin contains one card. Ford will then leave this room at which point you enter. If you are able to determine which card Ford gave to the guard, based only on looking at the bins, then, both you and Ford shall go free. Otherwise, you shall both remain imprisoned and forced to listen to Vogon poetry for the rest of eternity. Knowing this, can you and Ford think of a strategy that would guarantee freedom?

Neatly written or typed submissions may be emailed to Professor Jonathan Bloom ([email protected]). Submissions are due by 6 a.m. on Saturday, Feb. 22.