Make your parents promise to buy you a motorcycle
1. problem	You want a motorcycle, but your parents won't let you buy one.
2. intuition	Your parents are unlikely to simply agree to buy you a motorcycle. And it is unlikely that you can convince them to do so by cleaning your room, taking out the garbage, being nice to your little brother, etc. You need to get them to agree to buy you a motorcycle, without them knowing that they are doing so.
3. math	If your parents are true to their word, all it will take for them to agree to buy you a motorcycle is to have the following conversation with them. you "Will you promise to hug me if I make a true statement and not hug me if I make a false statement?" parents "Uh, sure." you "You will neither give me a hug nor will you buy me a motorcycle." That's it. Now, explain to your parents their options: Your parents hug you, but they don't buy you a motorcycle. If your parents hug you, then your statement ("no hug, no motorcycle") will be false. But your parents agreed not to hug you if you made a false statement -- so this option is no good. Your parents don't hug you, and they don't buy you a motorcycle. In this case, your statement ("no hug, no motorcycle") will be true. Your parents agreed to hug you if you made a true statement. But we just agreed above that they can't hug you -- so this option is no good. Your parents hug you, and they buy you a motorcycle. In this case, your statement ("no hug, no motorcycle") is false. But your parents agreed not to hug you if you made a false statement -- so this option is no good. And lastly, your parents don't hug you, but they buy you a motorcycle. In this case, your statement ("no hug, no motorcycle") is false. Since your parents agreed not to hug you if you made a false statement, there is no contradiction here. Option 4 is the only option that is consistent with your parent's promise, so they must buy you a motorcycle if they are to keep their promise to you. The above is an example of the application of a branch of mathematics known as logic. We can simplify the above statements with a few mathematical symbols: H = your parents hug you ~H = your parents don't hug you M = your parents buy you a motorcycle ~M = your parents don't buy you a motorcycle S = (~H and ~M) -- this is your statement T = a true statement F = a false statement Your parents promised that (if S=T then H) and (if S=F then ~H). We can now write the four options as follows (the symbols in red show the contradiction): (H and ~M) implies S=F implies ~H (~H and ~M) implies S=T implies H (H and M) implies S=F implies ~H (~H and M) implies S=F implies ~H Only option 4 has no contradiction.
4. summary	The above "trick" worked because we created a set of logical statements that led to contradictions in all but the desired conclusion. The logic of these statements is made particularly obvious when the statements are replaced with concise symbols. By the way, I doubt that this will actually convince your parents to buy you a motorcycle. But, maybe your parents will be sufficiently impressed with how clever you are, that you can convince them to buy you a video game as a consolation for them breaking their promise.

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