Game Theory [Back to A Mathematical Mosaic]

Elementary My Dear Watson!

Sherlock Holmes, master of logical deduction, chases a hardened criminal through Europe. One player plays the dashing and daring Holmes, and the other player plays the evil, nefarious, dastardly, reprehensible, unscrupulous, notorious criminal— hereafter denoted by the acronym, ENDRUN.
The Game
This battle of wits can be played in the airports of Europe. A less expensive alternative is to use the map on the opposite page. Each of the dots represents a city where the chase can take place, and the players can indicate their position by pointing at a city with a pencil or a pen. The straight lines indicate air routes where the players may travel. Sherlock Holmes begins in Stockholm, where he begins his famous chase. The criminal, ENDRUN, starts off in Paris, where he has just stolen the Mona Lisa. Each player, in his or her turn, may jump from one city to another connected by an air link. Holmes, being true and noble, goes first. If Holmes lands in the same city as ENDRUN, he captures the thief after an exciting and excessively destructive car chase and wins the game. If Holmes does not catch ENDRUN in fifteen or fewer moves, ENDRUN escapes and wins the game.

The Problem

This game is fixed. If you pick the right side, and play perfectly, you can always win, no matter how well your opponent plays. The big question is: who has the winning strategy? (And what is it?)

A Hint

This is less a hint than plain common sense. Don’t give up too soon! Try playing a few games with someone else, just to get a feel for how it works. Play both sides. Make a conjecture. Then try to figure out why it’s right (or wrong!).

© Brendan Kelly Publishing Email:
website updated October 16, 2005