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July 28, 2025, 03:33:36 am
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Author Topic: Coins  (Read 2602 times)  Share 

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TrueTears

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Coins
« on: July 02, 2009, 02:37:55 am »
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There are 12 coins. One of them is false; it weights differently. It is not known, if the false coin is heavier or lighter than the right coins. How to find the false coin by three weighs on a simple scale?
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Stroodle

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Re: Coins
« Reply #1 on: July 03, 2009, 08:06:37 pm »
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Put 4 coins on each side, if it doesn't balance, mix up the coins and start again from the beginning until they do balance :)

With the four coins left: {a,b,c,d} weigh a against b.
If a and b balances weigh a against c, if these balance then the false coin is d.
If a and b don't balance, then again weigh a against c, and if they don't balance then the false is a (if they do, the false is b).

If, at the start, the two lots of 4 coins don't balance then you could take 1 coin from the lighter pile and put it in the "standard" pile that wasn't weighed. Then take a coin from the standard pile and put it in the lighter pile. If you also swap a coin from the heavier pile with one from the lighter pile, then you can work out the false coin in two more weighs.
« Last Edit: July 04, 2009, 12:56:06 am by Stroodle »
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evaporade

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Re: Coins
« Reply #2 on: July 03, 2009, 10:28:59 pm »
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Start off with 3 coins on each side, .........
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kamil9876

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Re: Coins
« Reply #3 on: July 03, 2009, 10:45:37 pm »
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Here's another one for you coin fans:

You have 10 boxes with 10 coins each. All the coins from 9 of those boxes(all 90 of them) all weigh 1g. However the other box has coins which all weigh 1.1g. You have a scale that measures the weight of the load you put on. How can you determin which box has the 1.1g coins just by weighing one load of any combination of these 100 coins?
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

TrueTears

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Re: Coins
« Reply #4 on: July 03, 2009, 11:03:17 pm »
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Put one coin of the first box, two coins of the second box, 3 coins of the third box, etc etc etc, ten coins of the tenth box on the scale.
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kamil9876

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Re: Coins
« Reply #5 on: July 03, 2009, 11:16:47 pm »
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true, or 0 instead of 10 would work too. Meaning that I couldve been nasty and said that there are only 9 coins in each box :P
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Voltaire: "There is an astonishing imagination even in the science of mathematics ... We repeat, there is far more imagination in the head of Archimedes than in that of Homer."

TrueTears

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Re: Coins
« Reply #6 on: July 03, 2009, 11:19:01 pm »
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Quote from: kamil9876 on July 03, 2009, 11:16:47 pm
true, or 0 instead of 10 would work too. Meaning that I couldve been nasty and said that there are only 9 coins in each box :P
But you're nice, why would you do something like that to me?
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dcc

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Re: Coins
« Reply #7 on: July 04, 2009, 10:05:53 am »
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Over9000, I deleted your post because it was 'Spam'.  To everyone in this thread, please try to remain on-topic.
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