Puzzle: Can You Figure Out Which Steem Coin Is Fake? Part 2 [hard]

in puzzle •  7 years ago 

Your friend decides to challenge you one day, telling you that, "Hey, here's 12 Steem Dollar coins for you, but wait, one of them is fake. If you can figure out which of the twelve is fake, I will let you keep the 11 real coins and give you one more real coin. However, if you accept the challenge and can't find the fake coin, you'll have to give me 12 Steem Dollars instead.

You, a clever mathematician, thinks the problem should be easy to solve, and asks, "Sure, what's the catch?" To which your friend replies, "the terms of the challenge is that you may only use a scale 3 times to find out which of the twelve coins is fake."

How do you single out the fake coin?

Stuck? Hints:

  • The fake coin could be lighter or heavier than a real coin. You don't know.
  • You may only use the scale 3 times.
  • The scale can only be used to determine which side is heavier, lighter, or equal in weight.
  • There is no magic involved :)
puzzle logic fun
7 years ago by

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      ·  7 years ago 

    I guess this is a lot harder. Okaaay.
    So, I will divide the 12 coins into 3 groups. Coins A, coins B and coins C.
    First weighing, coins A and B.
    Result 1:
    If they balance this means the coins C contains the fake coin.

    1. Second weighing: There are 4 coins in coins C group; thus, 1 coin is fake. I would use 2 coins from either coins A and B group to weigh them with 2 coins from coin C.
      Result 1.1: If they balance, then the fake coin is either of the two remaining coins in coin C group.
      1.1 Third weighing: Label the remaining coins "Tom" and "Jerry". Weigh "Tom" against one coin from either Coin A or B. If that coin and "Tom" balances, then "Jerry" is the fake coin. If they don't, then "Tom" is the fake coin.
      Result 1.2: If they do not balance, then the fake coin is in that set of coin C coins.
      1.2 Third weighing: Label the coins "Chip" and "Dale". Weigh "Chip" against one coin from either Coin A or B. If that coin and "Chip" balances, then "Dale" is the fake coin. Otherwise, "Chip" is the fake coin.

    Result 2: If they don't balance, then I should take note which side is heavier and which is lighter.
    I will label coins in coins A group as 1, 2, 3 ,4 and coins from coins B as a, b, c, d. Suppose coins A is the heavy side.

    1. Second weighing: I will weigh a, 1, 2 against b, 3, 4.
      Result 2.1: If they balance, then the fake coin is either "c" or "d".
      2.1 Third Weighing: I will weigh "c" against one coin from the coins C group. If they balance, then "d" is the fake coin and if not, then "c" is the fake coin.
      Result 2.2: If they don't, I will again take note which side is heavier or lighter.
      Suppose a, 1, 2 is the heavier side and b, 3, 4 is the lighter side. Then the fake coin is either 1 or 2 and b. (If the heavier side is the lighter side and vice versa, I would do the same procedure with the corresponding coins.)
      2.2Third Weighing: I will weigh 1 against 2. If they balance, then "b" is the fake coin but if they don't, whichever is the heavy side is the fake coin.

    (If the heavier side is the coin B group, I will do the same procedure.)