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Find the Fake Coins Riddle
Posted by urikalish • 3/07/08 • Subscribe to this Discussion [RSS] • Report This Topic
A riddle:
There are 10 sacks of coins.
9 sacks contain real coins, and 1 sack contains fake coins.
A real coin weights 10 grams, and a fake coin weights 9 grams.
You have digital scales.
Can you identify the fake coins sack using one weigh only?
Note: You must solve it by yourself, no searching for the answer on the web.
User Comments
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Anybody?
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Yes, by adding one sack at a time to the scale until you get to the point where the sack you add is one gram shy.
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Can you identify the fake coins sack using one weigh only?
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that is just one weigh -
Exactly, I don't remove a sack I just keep adding one until the next one I add is short a gram. One weigh.
I win! Pay up. I take Euros. -
No, that's 10
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I think he means you only get one blunt weigh - no adding after that one weigh.
And I have no idea. I'd just take all the sacks with me at once - who cares about the weight?
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Hey, I am weighing those, argh!!
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just weigh the lightest one
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???
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sorry, uri. i was being silly and meant to pick up each one and put the "lightest" one on the scale.
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You check a coin from each sack by biting it, real gold is softer than fake and you weigh the one that is fake on the scale?
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Should I reveal the answer, or wait a little more?
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I want to know, even though I think I should have won with my first answer.
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use a magnet
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Is that frustration I'm detecting?
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nope ... sadly, it's simply a lack of attention span
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Do they contain an equal number of coins, or are the quantities unknown?-
An unknown number of coins in each sack.
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If anyone here can get this it is you, Tiffany.
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SPOILER WARNING!
I'll start, you'll finish. You take 1 coin from the first sack, 2 from the second, 3 from the third, etc. and...?-
OH.
Okay hopefully this is right but...
you proceed to take 1 coin from first, 2 from second, etc. until you have sets of 1,2,3,4,5,6,7,8,9,10 coins. This adds up to 550
Then you place the coins all on the scale and if you have 549 grams its the first bag, 548 its the second, etc. due to weights of the individual coins taken from the false bag being different from the weights of the normal coins.
I actually had a problem on a weird math quiz today that kind of involved the same thing. -
...a partridge in a pear tree?
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Correct!
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Wewt!
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Respect!
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Can I have the coins when you're finished with them?-
Maybe, if you'll answer this correctly:
I take one unknown coin (it might be real or fake), put it in an empty sack, and add one real coin to the same sack. Now there are 2 coins in the sack. I pull out one coin from the sack, test it, and find out it is real. What are the odds that the other coin in the sack is also real? -
You really do like talking about sacks...Just throwing that out there..
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So what's the answer?
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100%
hehe...I say that like I know, but I'm just guessing. -
1 in 2 (50%), 'cause I think you can simplify the problem into: "I put a coin into a sack, don't know whether it's real or fake (the coin, not the sack). Then I take it out again. What are the odds that it's real?" Well, it either is or it isn't real; so the odds are 1 in 2. The other coin is just smoke and lights in this problem.
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That's my instinct, too, but I've read enough to these threads to know that urikalish often has a statistical trick up his sleeve. Perhaps the answer is 66%,as you know the first was real but could have been the mystery coin (which means that the coin in the sack is the real one you put in) or the unknown coin could still be in the sack and may be either real or fake. -
The second problem (again):
I take one unknown coin (it might be real or fake), put it in an empty sack, and add one real coin to the same sack. Now there are 2 coins in the sack. I pull out one coin from the sack, test it, and find out it is real. What are the odds that the other coin in the sack is also real?
The solution:
SPOILER WARNING!
There are 4 possible scenarios:
1. I pulled out the coin known to be real – probability 0.5 (50%)
Now, the remaining coin is unknown so there are two options:
a. The remaining coin is a real – probability 0.5 (50%)
b. The remaining coin is fake – probability 0.5 (50%)
The total probability of 1.a is 0.5x0.5=0.25 (25%)
The total probability of 1.b is 0.5x0.5=0.25 (25%)
2. I pulled out the unknown coin – probability 0.5 (50%)
Now, the remaining coin is known to be real so…
a. The remaining coin is a real – probability 1.0 (100%)
b. The remaining coin is a fake – probability 0.0 (0%)
The total probability of 2.a is 0.5x1.0=0.5 (50%)
The total probability of 2.b is 0.5x0.0=0.0 (0%)
So, the total probability for the second coin to be real is the total probabilities of 1.a and 2.a which is 0.25+0.5=0.75 so the answer is 75%.
p.s. Using instinct/intuition when solving these kinds of problems should be your last resort.
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Hey, can you come over and balance my checkbook for me?
Pleeeeeeaaaaasseee? -
Sure
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hehehe good fun lucky me i got to the thread when all the answers were in -
I'm blushing ;-}
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No I don't know the weight of each sack?
so thats means you CANNOT find the weight at all
promomaker
www.promomaker.blogspot.com-
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