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May 1st, 2013, 06:21 PM  #1 
Newbie Joined: Oct 2012 Posts: 8 Thanks: 0  Face down paper strategy
Three pieces of paper each have one random number written on them. They are placed upside down on a table. The objective is to choose the slip with the highest number on it. The rules are: You may turn over any one of the three papers and look at its number. If you think it is the highest, then keep that paper and stop. Otherwise, discard that paper and choose a second one. You may then either keep the second one or discard it and take the last paper, in which case you must keep that one. 1. Is there any strategy you may use to increase your chances of winning, or will it make no difference how you play the game? 2. If there is a superior strategy, describe it. If there is none, then explain why. 
May 1st, 2013, 06:54 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,885 Thanks: 1088 Math Focus: Elementary mathematics and beyond  Re: Face down paper strategy
If you turn over a sheet and discard it in favor of another, what do you know about the two numbers? From that, what is the probability that the third sheet, or the second sheet (given it is higher than the first) is the highest number? If you keep the first sheet, what is the probability it is the highest?

May 1st, 2013, 08:09 PM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,622 Thanks: 954  Re: Face down paper strategy
All numbers > 0 ? All numbers different? Is there a limit? Or is 100000000000000000000000000.........00000000000000 000000000000000 possible? 

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