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# Weighing I.

27 replies to this topic

### #1 rookie1ja

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Posted 30 March 2007 - 06:00 PM

Weighing I. - Back to the Water and Weighing Puzzles
You have 10 bags with 1000 coins each. In one of the bags, all coins are forgeries. A true coin weighs 1 gram; each counterfeit coin weighs 1.1 gram.
If you have an accurate scale, which you can use only once, how can you identify the bag with the forgeries? And what if you didn't know how many bags contained counterfeit coins?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.
Pls visit New Puzzles section to see always fresh brain teasers.

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### #2 kola

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Posted 20 April 2007 - 05:33 PM

If we dont know how many bags has faulty coins, then min number of coins from bag i = 2 * number of coins in bag i-1.

Therefore, the sequence would be

1, 2, 4, 8, 16, 32, 64, 128, 258, 512.

Basically, represent the weight difference divided by 0.1g in binary numbers and positions of 1 will give you which bags have faulty coins.
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### #3 vinay0007

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Posted 08 May 2007 - 02:44 PM

Binary series is more precise.. which depicts.
2^0, 2^1, 2^2.... so on.
and whatever the extra weight it will be simple for the calculation..
100101010 format
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### #4 Garrek99

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Posted 17 May 2007 - 12:56 AM

This sequence won't work:

1, 2, 4, 8, 16, 32, 64, 128, 258, 512.

Here is why. If the 10th bag only is full of fakes you'll get an extra weigh amount of 51.2g.
And, if bags 2-9 are fake then you'll get (25.8+12.8+6.4+3.2+1.6+.8+.4+.2) 51.2g and then you won't be able to tell which situation you are in.

The total extra sum has to be distinct for any combo of fake bags.
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### #5 Baikin

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Posted 29 May 2007 - 06:34 AM

There's a mistake on that sequence, so there's also a mistake on proving it wrong.

The sequence should be:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and so on. This sequence should meet the mentioned conditions.
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### #6 Camshaft

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Posted 03 July 2007 - 07:35 PM

Place all bags on the scale, it should read 10,100g. Take off a bag until the 100 at the end goes away. That will be the bag with the forgeries. If you don't know how many bags contain the forgeries, then still place all bags on the scale and every time 1,100g is removed from the weight that bag will be full of forgeries.
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### #7 Garrek99

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Posted 09 July 2007 - 12:26 AM

Place all bags on the scale, it should read 10,100g. Take off a bag until the 100 at the end goes away. That will be the bag with the forgeries. If you don't know how many bags contain the forgeries, then still place all bags on the scale and every time 1,100g is removed from the weight that bag will be full of forgeries.

You are given one opportunity to use the balance. Your method requires 1 or more tries.
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### #8 puppyluv1725

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Posted 21 July 2007 - 06:15 AM

you know
all these weird riddles and stuff make my brain hurt like heck
can you make them a bit clearer and not so hard
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### #9 pilgrim

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Posted 12 October 2007 - 09:42 AM

It's a good one
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### #10 luioliher

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Posted 20 November 2007 - 03:45 PM

You can always open the bag
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