Imagine that one day Steem has become mainstream, and that governments issue Steem coins.
One day, 12 of the wealthiest whales decide to donate 1 Steem Dollar each to a charity fund for the minnows. The coins are gathered and put into a pile like so:
Just as the coins are about to get deposited, someone from the charity with a high sense of intuition thinks that one of the coins is fake and halts the transaction. He also senses that the counterfeit coin is heavier than the real coin.
It just so happens that you are the charity's greatest mathematician, and you decide to use this scale to find out which of the 12 coins is fake. Since you're so clever, you give yourself the additional challenge of only using the scale a maximum of 3 times.
How do you single out the fake coin?
Stuck? Hints:
- You may assume that the fake coin is heavier than the real coin.
- 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 :)
First, I divide the 12 coins equally and weigh them. I will again divide to equal numbers whichever half is heavier and weigh them. Now, I'll isolate the 3 remaining coins that are heavier. I'll label them 1, 2, and 3. I'll choose two coins to weigh. If I weigh 1 and 2, and one is heavier, then that'll be the fake coin. If 1 and 2 are equal in weight and are balanced, then the 3rd coin is the fake coin.
It was a fun puzzle game. Thanks @nafion.
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Nice answer!
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Your post was opened in my laptop for a while. I was constructing my solution and simultaneously typing about it. I didn't realized too many people answered already. Hahaha.
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Hahaha, ready to tackle the harder version?
https://steemit.com/puzzle/@nafion/puzzle-can-you-figure-out-which-steem-coin-is-fake-part-2-hard
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Oooh. That's intense. Gonna check it out, now. Sorry for being late.
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Put 6 in each, split the heavier side in two times 3 coins and set aside the other 6. See which of the set of 3 coins is heaviest, set aside the others. Now put two of the three coins on one side each. Is one heavier, that's your fake one. Are they both equal, then the one you didn't put in is the fake one.
Fun puzzle :D
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Nice! Glad you had fun :)
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There's a harder version :)
https://steemit.com/puzzle/@nafion/puzzle-can-you-figure-out-which-steem-coin-is-fake-part-2-hard
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Oh gosh, harder indeed! I don't know how to solve that one :o
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On the first measure you put 4 coin in a plate of the scale and other 4 in the other plate. If one of the plates is heavier then the fake coin is one of this. If not, the heavier coin is in one of the other 4 not measured coins.
Then you put 2 of the coins that may be fake in a plate and the other 2 in the other. The heavier plate has the fake coin.
Finally you put each of the coins in the plate and the heavier one is the fake.
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That works!
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Want to try to solve the harder version of the puzzle?
https://steemit.com/puzzle/@nafion/puzzle-can-you-figure-out-which-steem-coin-is-fake-part-2-hard
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