You have 12 coins, one of which is fake. The fake coin is indistinguishable from the rest except that it is heavier. Can you determine which is the fake coin heavier using a balance scale and only 3 weighings?

Yep! 
Weighing #1: Start off by splitting the pile of 12 coins evenly into two piles, 6 in each pile. Put one pile on each side of the balance. The side that is weighed down has the fake coin it in. Ignore the other 6 coins.

Weighing #2: Now you have 6 coins left. Split the pile evenly again, 3 in each pile. Repeat the same process and put each pile on one side of the balance. The side that is weighed down has your fake coin in it. Ignore the other 3 coins.

Weighing #3: You have 3 coins left. Take two coins, whichever two you like, and weigh them. If they weigh the same, then the one you didn't weigh is the fake one. If one is heavier, then that heavier one is your fake coin.