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Can you solve below mathematical equation?

2^1234 - 2^1233

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John is on an island and there are three crates of fruit that have washed up in front of him. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

Each crate is labelled. One reads 'apples', one reads 'oranges', and one reads 'apples and oranges'. He know that NONE of the crates have been labeled correctly - they are all wrong.

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Crossword puzzles

In the 1920s, people feared that crossword puzzles would contribute to illiteracy.