This problem is a combination of a traditional weights and scales puzzle and a probability puzzle.

You are given the traditional scale balance and a set of 10 coins. You know that in this set of coins there are four fakes - two that are heavier than the others, and two that are lighter. Furthermore, you know that a light coin plus a heavy coin will perfectly balance two genuine coins. You are permitted only two weighings with the balance and asked to pick one of the 4 fake coins. What strategy should you use to maximize your success rate, and what would your success rate be?

What if you were given one genuine coin to start with (though still leaving you with 10 unknown coins)?

I really like this problem  A real thinker.  I did not even attempt a solution though (my IQ keeps me from attempting it).  I liked it immediately when reading it and even more so after reading the comments and solution.

Posted by john on 2005-04-06 17:33:28