Puzzle 17

This puzzle was stole… er… I mean…. paraphrased from the Car Talk puzzle archives. I think that’s all for a bit from them cause I already have a puzzle lined up for the next two weeks. I’ll give the answers this time cause it isn’t practical for a password answer.

Three different numbers are chosen at random, and one is written on each of three slips of paper. The slips are then placed face down on the table. The objective is to choose the slip upon which is written the largest number.

Here are the rules: You can turn over any slip of paper and look at the amount written on it. If for any reason you think this is the largest, you’re done; you keep it. Otherwise you discard it and turn over a second slip. Again, if you think this is the one with the biggest number, you keep that one and the game is over. If you don’t, you discard that one too.

I know of a strategy that will, instead of a 1 /3 chance, give a 1/2 chance of chosing the right card and it’s the only strategy that does this. What is it?

Post your answer in the comments. Have fun!

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One Response to Puzzle 17

  1. James says:

    Here’s how to do it: First, you pick one of the three slips of paper at random and look at the number. No matter what the number is, you throw the slip of paper away. But you remember that number. If the second slip you choose has a higher number than the first, you stick with that one. If the number on the second slip is lower than the first number, you go on to the third slip.

    Here’s an example. Let’s say for the sake of simplicity that the three slips are numbered 1000, 500, and 10.

    Let’s say you pick the slip with the 1000. We know you can’t possibly win because, according to the rules, you’re going to throw that slip out. No matter what you do you lose, whether you pick 500 next or 10. So, you lose —twice
    0/2

    Now if you pick the 500 first you will win. if you pick 10 you throw it away and get the 1000. if you pick 1000 you keep it according to the rules.
    2/4

    If you pick 10 first you have a 1 in 2 chance of winning. If you pick 500 next you lose but if you pick 1000 next you win.

    Final total: 3/6 or 1/2

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