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
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 20131019 13:26:21 