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8th Grade · Twelve Coins

Thirteen is old enough for the most useful habit an adult has: proving a thing is possible before spending a week looking for how.

Full screen — no distractions

Where this goes

The ladder

The same idea, three times, roughly a year apart. This is what depth looks like from the outside.

  1. This year

    Twelve coins, three weighings, direction unknown.

  2. Next year

    The general rule: n weighings handle (3ⁿ − 3)/2 coins. Derive it rather than look it up.

  3. The year after

    Information theory — and the discovery that this puzzle and file compression are the same puzzle.

What lives on the desk this year

  • A sheet large enough for the whole tree
  • Coins and a balance
  • A ruler, for drawing branches straight
  • A folder of proofs you wrote yourself
  • A question you have been carrying for months

All twelve years

A tower that has to stay up while you count to ten, at three. A proof that no list can contain the real numbers, at fifteen. Same practice, twelve sizes.

Last updated: September 2026

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