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

Ady, taking your hint, I looked at some possibilities (for minutes not hours) and I still am thinking that there are conditions that cannot be separated by blind logic??

using sets of 33, 33 , and 34, you have to weigh the 2 33's because otherwise you can't learn anything for certain.

For example
1st pile has 33 total, 2 fake, weigh against second 33 with 1 fake.  I don't see a second weighing that can sort this out to the point where you can pick at least one real coin with 100% certainty.

The problem lies with only knowing that one side is heavier (lighter) then the other, but not by how much (i.e. how many fakes).

I can't wait to see the answer posted.

Posted by Kenny M on 2013-10-20 10:23:43