#23

You have 9 gold coins. All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. You have a scale - balance type with 2 trays - but can only load it twice. How do you find the fake gold coin?

Answer:

Take any 8 of the 9 coins, and load the scale up with four coins on either side. If the two sides are equal, then the remaining coin is the fake.
If however, the two sides are not equal, then that remaining coin is a real coin and the fake is in one side or the other of the scale. The trick is that now you must unload at the same time a single coin from each side of the scales. If the scales now balance, the bad coin is one of the two which you just withdrew. If the scales remain unbalanced, the fake is still on the scales. As you remove good coins you can just add them to the good coin pile which began with the first isolated coin. Once you have found the two coins which when removed balance the scales, or if they are the final two and the scales are still unbalanced, you take one of those two and weigh it against a known good coin. If they balance on this second loading of the scales, or if the don't, you have now with only two loadings of the scales correctly identified the fake coin.