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Huge Numbers & Infinity

Numbers so big your brain says no: doubling, giant sums and things that never end.

10 puzzles

  1. Ages 10–12🔁 Another number ×4

    A teacher wanted a quiet hour, so she told the class: "Add up every number from 1 to 100. No talking until you finish." One boy put his slate down after a few seconds, and his answer was right. How could he possibly be that fast?

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  2. Ages 10–12🔁 Another number ×4

    A king offers the inventor of chess any reward he likes. The inventor asks only for rice: one grain on the first square of the board, two on the next, and double again on every square after that. The king laughs at such a cheap prize, so who do you think ends up sorry?

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  3. Ages 10–12

    Every time you fold a sheet of paper in half, it gets twice as thick. Paper is so thin that this doesn't sound like much. If you could fold it just ten times, how thick would it be?

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  4. Ages 8–10🔁 Another number ×4

    Start a stopwatch right now and let it tick, one second at a time. When it finally reaches one million seconds, what will you be doing?

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  5. Ages 10–12🔁 Another number ×4

    Put two fingers on your neck and feel your heart: it beats about 70 times a minute, even while you sleep. One day it will beat for the billionth time. How old will you be?

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  6. Ages 12–14

    Put a nine after the decimal point and you get a number just below one. Add another nine, and another, and it's still just below one. But what if the nines never, ever stop: is 0.999… still smaller than 1?

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  7. Ages 12–14

    A hotel has an endless corridor of rooms, numbered one, two, three and on forever, and tonight every room has a guest. A tired traveller walks in and asks for a bed, and the owner smiles: "No problem!" How can he fit her in without anyone sharing a room?

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  8. Ages 8–10🔁 Another number ×4

    Friends keep ringing your doorbell, and every new arrival shakes hands with everyone already at the party. Nobody gets skipped, and nobody shakes the same hand twice. Once ten friends are there, how many handshakes have happened?

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  9. Ages 12–14

    Imagine counting every atom in the whole universe: in every star, every planet and every grain of sand. Now picture a googol, a 1 followed by a hundred zeros. Which is bigger, and by how much?

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  10. Ages 12–14

    You stand facing a wall. You walk half of the way there, then half of what's left, then half of what's left again, and you never stop. Do you ever reach the wall, and how far do you walk altogether?

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