# Fake and genuine coins

There are 14 coins, numerated from 1 to 14, and presented as an evidence at the court. The first 7 are fake coins, and others are genuine coins. Fake coins have all the same weight and they are lighter than the genuine coins. How can an expert prove that the first 7 coins are fake, and that other coins are genuine, using balance, in at most 3 weighings? ( We don't know whether the genuine coins have the same weight, but if someone can solve problem in case when they have the same weight, I would appreciate it.)

• Does the jury already know that the first 7 coins are all the same weight? (My interpretation of the question as it stands: no, they don't.) Commented Jan 5, 2018 at 17:31
• I suppose they don't know. Commented Jan 5, 2018 at 17:34
• user122, do you know a solution to this question? Commented Jan 5, 2018 at 17:37
• @GarethMcCaughan that was exactly what I was going to ask. Commented Jan 5, 2018 at 17:37
• Sorry to repeat myself, but could you tell us where the problem comes from? Two reasons. First, I can't help suspecting that there may be some inaccuracy in how it's stated, and checking the original might help. Second, we do generally insist around here on giving credit where it's due. Thanks! Commented Jan 5, 2018 at 18:03