probability question

["Leeds, Mark" <mleeds@mlp.com>]

i've seen the following question before but

i don't remember how to do it so

i was wondering if anyone knows

where i can find the answer. i'm

not asking anyone to do it because

i know it's published somewhere.

 

you have a game : each turn,

a random number is chosen

between 1 and 100  ( assume uniform distribution )

and given to you. you can either

 

A) accept the number and stop  the game

and decide that the number you received is

your number.

 

B) throw out that number ( but you

can't claim it later ) and try for another number

 

you get say, 20 turns ( numbers

are chosen with replacement ) and you

want to maximize your value where

your value is the number you receive when

you choose to stop.

 

what is the algorithm for deciding when to stop ?

 

sorry to bother everyone.

 

 

                                                        mark