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Take the right one (Posted on 2013-10-18) Difficulty: 3 of 5
Among 100 coins exactly 4 are fake. All genuine coins weigh the same; all fake coins, too. A fake coin is lighter than a genuine coin.

How would we find at least one genuine coin using two weighings on a balance scale?

Source: 2010 Euler math Olympiad in Russia- authored by A.Shapovalov

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Hints/Tips 99 coins | Comment 10 of 18 |
I find it very interesting that the number of coins to start is so significant.  If there were 99 coins, and six were fake, the task would still be possible.  If there were 97 coins, and four were fake, I'm not sure it would be possible.

 
Edit: actually 99 and 6 may not be possible.  I found a problem in my answer.  97 and 4 does appear possible.

Edited on October 19, 2013, 1:28 pm

Edited on October 19, 2013, 1:30 pm
  Posted by Tristan on 2013-10-19 13:26:21

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