MH
MH
Arjun Shastry wrote:This puzzle I got in in Russian Math book.
There are 14 coins. Seven of them are counterfeit and are lighter than genuine ones.All counterfeit coins are of equal weight.
In only three weighings, you have to find which seven coins are counterfeit(lighter).
MH
Arjun Shastry wrote:There are 14 coins. Seven of them are counterfeit and are lighter than genuine ones.All counterfeit coins are of equal weight.
In only three weighings, you have to find which seven coins are counterfeit(lighter).
Arjun Shastry wrote:I also think whether it has any solution.This is the exact problem statement(I made mistake by saying all lighter coins weigh same) Fourten coins were represented in a court as evidence.The judge knows that exactly 7 of these are counterfeit and weigh less than genuine coins.A lawyer claims to know which coins are counterfeit and which are genuine and she is required to prove it.
How can she accomplish this using only three weighing?
Misha Ver wrote:These are two completely different puzzles The former has not solution, but the latter has.
MH
Steve Fahlbusch wrote:It can be done in 2 weighings
Steve Fahlbusch wrote:Given the problem statement, it can be done in 2
Steve Fahlbusch wrote:It is only assumed that we weigh coins against each other on a balance scale. What if we simply have a spring scale. Since the lawyer would have to place the weight of a genuine coin into evidence, the weigh 1 counterfit  show that it is less than the official published weight of a genuine code. Then weigh all 7 counterfit coins. If it is seven times the one, we have proven that we know which are the seven good / bad coins.
This of course assumes that all bad coins weigh the same. And that all good coins weigh the same.
SCJA
When I die, I want people to look at me and say "Yeah, he might have been crazy, but that was one zarkin frood that knew where his towel was."
Steve Fahlbusch wrote:This of course assumes that all bad coins weigh the same. And that all good coins weigh the same.
"I'm not back."  Bill Harding, Twister
W. Joe Smith wrote:I thought the assumption was you didn't know which ones were counterfeit, so you were weighing them to find out?
Arjun Shastry wrote:I also think whether it has any solution.This is the exact problem statement(I made mistake by saying all lighter coins weigh same)
Fourten coins were represented in a court as evidence.The judge knows that exactly 7 of these are counterfeit and weigh less than genuine coins.A lawyer claims to know which coins are counterfeit and which are genuine and she is rquired to prove it.
How can she accomplish this using only three weighings?
Taken from this book http://www.amazon.com/MathematicalCirclesRussianExperienceWorld/dp/0821804308
"I'm not back."  Bill Harding, Twister
Jim Yingst wrote:
W. Joe Smith wrote:I thought the assumption was you didn't know which ones were counterfeit, so you were weighing them to find out?
No, that was the original, misstated version of the problem. It's impossible in 3 weighings. Arjun posted the corrected version on November 25/26:
Arjun Shastry wrote:I also think whether it has any solution.This is the exact problem statement(I made mistake by saying all lighter coins weigh same)
Fourten coins were represented in a court as evidence.The judge knows that exactly 7 of these are counterfeit and weigh less than genuine coins.A lawyer claims to know which coins are counterfeit and which are genuine and she is rquired to prove it.
How can she accomplish this using only three weighings?
Taken from this book http://www.amazon.com/MathematicalCirclesRussianExperienceWorld/dp/0821804308
SCJA
When I die, I want people to look at me and say "Yeah, he might have been crazy, but that was one zarkin frood that knew where his towel was."
"I'm not back."  Bill Harding, Twister
rutuja patil wrote:Jim, what if they don't know the exact weight... then will they need two weighings?
and you said"Thus, the remaining seven coins must be counterfeit", no, they might be counterfeit, they might contain some genuine coins, you can not say'must' without weighing remaining seven coins...
rutuja patil wrote:Jim, what if they don't know the exact weight... then will they need two weighings?
"I'm not back."  Bill Harding, Twister
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