
Re: A rational X irrational game
Posted:
Mar 19, 2004 10:49 AM


On 19 Mar 2004 07:30:09 0800, artur@opendf.com.br (Artur) wrote:
>Hello >I've been thinking about the following problem (or puzzle) but hasn't >come to a conclusion yet. Maybe someone can give a hint. > >A and B are playing the following game: On the real line, A chooses a >closed interval I1 of length 0<L1<=1. Then, B chooses a closed >interval I2, of length 0<L2<=1/2, contained in I1. Then A, in turn, >chooses a closed interval I3, of length 0<L3<=1/3, contained in I2, >and so on. We know there's one, and only one, real number x that >belongs to all of the intervals I1, I2, I3.... If x is rational, A >wins the game, and if x is irrational, then B wins. We are asked to >find an strategy that B should follow so that he will certainly win >the game no matter how B chooses his intervals. > >Since the rationals are countable and the irrationals are not, it >really seems that there is such a strategy that assures B will ever >win, but I couldn't find it so far.
Hint: B doesn't have to force a win on the first move. On the first move B prevents one way he can lose, on the next move he prevents another method of losing...
>Thank you. >Artur
************************
David C. Ullrich

