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Author Topic: Riddle - you have 12 coins, one of which is counterfeit...  (Read 5815 times)

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Offline Neil Obstat

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Riddle - you have 12 coins, one of which is counterfeit...
« Reply #15 on: July 09, 2016, 05:48:00 PM »
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  • Quote from: Neil Obstat
    If the first pass balances and the second pass does not balance, how many real coins are you left with now?

    pass 1: 4 vs. 4 --> balances ............... 8 good coins
    pass 2: 2 vs. 2 --> not balanced ......... 9 good coins  (How do you know have 9 good coins?)

    For pass 2, which coins are on the left side of the scale and which are on the right?
    Remember, you have to set aside one of the 4 that were set aside during pass 1.
    So you're only weighing 3 of those 4, therefore, where do you get 2 vs. 2 with only 3 coins?


    On the second pass, above, you get 2 vs. 2 with only 3 coins because you did not put all 4 coins on the scale.

    When the first pass balances, and you have 8 good coins, the 4 you had set aside are entirely unidentified as to which is CF. Therefore, for the second pass, you must set aside one of the 4 coins. Put two of them on the left side of the scale, and one of them on the right side. Borrow one of the 8 known good coins and put it on the right side of the scale, so you have 2 vs. 2, and one coin set aside, off the scale.

    If the scale does not balance now (second pass) you know the coin you set aside is a good coin (not CF), and that's how you now have 9 good coins when pass 2 does not balance. Furthermore, you know that the two coins on the left side are earmarked LIGHT (if the scale went up on the left) if counterfeit, AND the one coin on the right (not the good coin) is earmarked HEAVY (if the scale went up on the left) if CF.

    These 3 coins are now "earmarked" because you need one more turn at the scale to settle which coin is counterfeit, and when you know which one it is, you will also know whether it is heavy or light because of its 2nd pass earmark.

    There is one more trick left, for the 3rd pass.  Do you know what that is?

    (The first trick was setting one coin aside for the second pass and replacing it with a known good coin for the purpose of working the scale.  You must make a similarly innovative change in your arrangement for the third and final turn at the scale. What do you change this time?)

    If you can answer these questions correctly, you will be preparing yourself to solve the problem of what to do when your first pass does not balance.

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    Offline Neil Obstat

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    Riddle - you have 12 coins, one of which is counterfeit...
    « Reply #16 on: July 11, 2016, 11:21:45 PM »
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  • Quote from: JohnAnthonyMarie
    this is a good riddle, and  I will patiently await the resolution.

    I thought it's good too, but nobody's posting any questions.

    Maybe you'll be waiting a long time. Or, you could ask a question.
    .--. .-.-.- ... .-.-.- ..-. --- .-. - .... . -.- .. -. --. -.. --- -- --..-- - .... . .--. --- .-- . .-. .- -. -.. -....- -....- .--- ..- ... - -.- .. -.. -.. .. -. --. .-.-.