PROBLEM:
Given twelve marbles that are identical in size, shape, and color, determine which single marble is heavier in weight than the others.  You are supplied with a balance and must conclude your determination in three weighings
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SOLUTION:
First, weigh all 12 marbles, 6 on each side of the scale (weighing #1).  Whichever side is heavier, take those 6 marbles and weigh 3 on each side (weighing #2).  Again, whichever side is heavier, take those 3 marbles, placing 1 to the side, and weighing the other 2, one on each side of the scale (weighing #3).  During this weighing, if one marble weighs heavier than the other, the answer is obvious, and so too, if they balance perfectly, then the marble you put to the side is the heavier marble!