Beach Day by Rodger Bliss
September 2023
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Numbers Game

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. Then you’re stuck with the third. There‚Äôs no going back.

The chance of getting the highest number is one in three. Or is it? Is there a strategy by which you can improve the odds?

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2 guesses to Numbers Game


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  • brent

    Look at the 1st number and throw it away.
    Look at the 2nd number – if it’s larger than the 1st. Keep this number – you have 50% chance of it being the biggest.
    If the 2nd is smaller than the 1st, discard the 2nd number and keep the 3rd.

    Assuming the 3 numbers can be called “Small” “Medium” and “Large” They will be in one of the following 6 orders:
    SML – we toss S and keep M – we loose.
    SLM – we toss S and Keep L – we WIN!
    MSL – we toss M, toss S and keep L – WIN
    MLS – we toss M, keep L WIN
    LSM – we toss L, toss S keep M – lose.
    LMS – we toss L, toss M keep S – lose.

    With this method, we have a 3/6 (or 1 in 2) chance or 50% chance of getting the highest number.

  • A very excellent answer to a complex problem Brent! You are today’s winner and a master of a difficult unsolved riddle.