# Coin weights game theory

http://blog.tanyakhovanova.com/?p=279

This is an extension of the problem posted here.

You have 14 coins. You know that 7 are real, and 7 are counterfeit. The real coins are 1000g, and the fake coins are 999kg.

You have a balance accurate enough to do the measurement. However, this balance is a peculiar balance. Assume that if you weigh multiple coins, you do not place them incrementally. That is, if you weigh 3 coins against another 3 coins, you would place all the coins in the balance scale at the same time.

1)If the weight one one side is heavier, the balance incinerates one coin selected at random from the heavier side. (Recall that the real coins are heaver than the fake ones). 2)If the weight is equal, you take back all the coins.

Find a methodology in which one can necessarily identify a single real coin that has not been incinerated. Either find the strategy, or prove that such a strategy does not exist.

• Welcome to MathSE. I see that this is your first question. So I wanted to let you know a few things about MathSE. Posting questions in the imperative (i.e. Compute all such, Prove that...), is considered rude by some of the members, so it would be nice of you to change that wording; perhaps by adding what are your thoughts or what you have tried in trying to answer the problem. These sort of pleasantries usually result in more and better answers. Thank you. – Arturo Magidin Oct 7 '11 at 20:00
• That's some heavy coinage. – Henning Makholm Oct 7 '11 at 20:44
• See #4 here usamts.org/Tests/Problems_23_1.pdf from an ongoing contest. nice one. – user17294 Oct 8 '11 at 3:17
• My goodness. This was given to me by a student of mine (I am a teacher). I am sorry for any inconveniences... – Stewart Oct 8 '11 at 12:27
• I will adhere to this in the future. Thank you. – Stewart Oct 8 '11 at 12:43