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'm afraid I don't follow.
Say the 2 weighings are equal. The 2424 equality occurs if the 2 coins set aside originally and the 49th coin not used in the second weighing are the same, all normal or all light. In the first case the coins on each side are 23 normal and 1 light, in the second 24 normal. How do you tell the cases apart?

Posted by xdog
on 20131019 21:35:46 