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Math Help - Weighing in...

  1. #1
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    Weighing in...

    6 coins: four weigh 2 units each, one weighs 1 unit and one weighs 3 units.

    NO: you can't tell if one is heavier by picking 'em up!

    But because of that, you are given a pan scale.

    How many weighings (at minimum) will you need in
    order to locate the 1-unit and the 3-unit coins?

    NO guessing! Show your method.
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  2. #2
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    Here is my attempt

    Spoiler:


    Divide the 6 into two piles. Weigh them against each other. (1 weighing)

    If they are equal, this means that that the two weird coins are on the same side. Pick one side and weigh 2 of the coins (2nd weighing). If they are the same, then the 2 weird coins are on the other side. The other side are coins a,b and c. Pick a and b. They cannot be equal. Weigh them. One is bigger than the other, say b>a. Weigh b with c (3rd weighing).

    If b< c, then the 1 unit coin is a and the 3 unit coin is c. If b >c, then b = 3 units. Then weigh a and c to get which one is smaller and that's the 1 unit coint. (4 weighings in the worst case scenario).

    Now, if after the first weighing, the 2 sides a different, we must have have that the heavier side contains the big coin and the lighter side contains the smaller coin. Weigh two coins on the heavy side to get which one is 3 units (2nd weighing). That is if they are equal, it's the third, and if they are not, then it's the heavier one. Same on the other side - weigh two coins on the light side to get which one is the 1 unit coin (3rd weighing).


    So, worst case scenario, we must have 4 weighings.
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  3. #3
    MHF Contributor
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    Agree...
    I simply couldn't beat 4 weighings.
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