There are five bags of gold that all look identical, and each has ten gold pieces in it. One of the five bags has fake gold in it. The real gold, fake gold, and all five bags are identical in every way, except the pieces of fake gold each weigh 1.1 grams, and the real gold pieces each weigh 1 gram. You have a perfectly accurate digital gram scale and can use it only once. How do you determine which bag has the fake gold?
Answer: See below.
Explanation: Take one gold piece from the first bag, two from the second bag, three from the third bag, four from the fourth bag, and five from the fifth bag. If the weight on the scale ends in .1, then you know the first bag has the fake gold. If the weight on the scale ends in .2, then the second bag has the fake gold, and so on and so forth.