Monday, 22 March 2010

An Answer for Monday

Yesterday I posed a question, lifted from Simon Singh's book "Fermat's Last Theorem". The puzzle was related to Game Theory, which uses Mathematics to explain how people play games. Using Game Theory could give competitors (or enemies) an edge when playing (or waging war).

The answer to the query posed is:

Mr Black's options are:

"First, Mr Black could aim at Mr Grey. If he is successful, the next shot would be taken by Mr White. Mr White has only one opponent left. Mr Black, and as Mr White is a perfect shot then Mr Black is a dead man.

A better option is for Mr Black to aim at Mr White. If he is successful, then the next shot will be taken by Mr Grey. Mr Grey hits his target only two times out of three and so there is a chance that Mr Black will survive to fire back at Mr Grey and possibly win the truel.

It appears that the second option is the strategy which Mr Black should adopt. However, there is a third and even better option. Mr Black could aim into the air. Mr Grey has the next shot and he will aim at Mr White, because he is the more dangerous opponent. If Mr White survives then he will aim at Mr Grey because he is the more dangerous opponent. By aiming into the air, Mr Black is allowing Mr Grey to eliminate Mr White or vice versa.

This is Mr Black's best strategy. Eventually Mr Grey or Mr White will die and then Mr Black will aim at whoever survives. Mr Black has manipulated the situation so that, instead of having the first shot in a truel, he has first shot in a duel."

So, did you get it right?...


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