You have two jugs, one that holds exactly 3 gallons, and one that holds exactly 5 gallons. Using just these two jugs and a fire hose, how can you measure out exactly 4 gallons of water?
Fill the 5-gallon jug to the top, and then pour it into the 3-gallon jug until the 3-gallon jug is full. You now have 2 gallons remaining in the 5-gallon jug. Pour out the 3-gallon jug, and then pour the 2 gallons from the 5-gallon jug into the 3-gallon jug. Finally, fill the 5-gallon jug to the top and pour it into the 3-gallon jug until it's full. Since there was only space left for 1 more gallon in the 3-gallon jug, you now have exactly 4 gallons in the 5-gallon jug.
Our dinner guests cry that we are evil, when they notice their place in the meal. But its no big deal why; we are just one big happy tribe! And we get really fed up with people!
Who, What or Are we?
Consider the following explanation for why 1=2:
1. Start out Let y = x
2. Multiply through by x xy = x2
3. Subtract y2 from each side xy - y2 = x2 - y2
4. Factor each side y(x-y) = (x+y)(x-y)
5. Divide both sides by (x-y) y = x+y
6. Divide both sides by y y/y = x/y + y/y
7. And so... 1 = x/y + 1
8. Since x=y, x/y = 1 1 = 1 + 1
8. And so... 1 = 2
How is this possible?
Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not followinng basic mathematical rules, we are able to get strange results like these.
General Custer is surrounded by Indians and he's the only cowboy left.
He finds an old lamp in front of him and rubs it. Out pops a genie. The genie grants Custer one wish, with a catch. He says, "Whatever you wish for, each Indian will get two of the same thing." Custer ponders a while and thinks:"If I get a bow and arrow they get two. If I get a rifle they get two!" He then rubs the bottle again and out pops the genie. "Well," the genie asks "have you made up your mind?"
What did Custer ask for to help him get away?
