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)?

Weighing one coin against two others in two separate weighings, I calcualted about a 50% chance over all of picking a fake by picking a coin out of the weighed 3 or unweighed 7 depending on the weighing results.

Similar to Lewis I guess. I'm not going to show my work, since there is reams of it. Weighing more than one coin at a time scares the dickens out of me.

Posted by ryan smith on 2003-08-07 01:05:53