On a quiz show, you can pick two envelopes. One envelope has $1000 in it, one has $500, one has $300, one has $200, one has $50, and one is empty. How many different amounts can be won?

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This classic brain teaser requires a systematic approach to uncover every possible outcome. If you were to list all the possible pairs of envelopes you could pick, you would find there are 15 different combinations. You could pair the $1000 envelope with each of the other five, then pair the $500 envelope with the four remaining smaller amounts, and so on,

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