Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: A rational X irrational game
Replies: 10   Last Post: Mar 20, 2004 5:52 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: A rational X irrational game
Posted: Mar 19, 2004 10:49 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.