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7th Grade · The Bridge at Night

Twelve is when a child can be shown that the sensible plan — always take the cheapest next step — is a trap with a name.

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

    Four walkers, 17 minutes.

  2. Next year

    Any number of walkers, and the rule for deciding which pairing to use.

  3. The year after

    Greedy algorithms and why they fail — the same idea that runs inside a satnav.

What lives on the desk this year

  • Index cards, one per person in the puzzle
  • A whiteboard you can wipe without guilt
  • A timer
  • A folder of plans that did not work, kept on purpose
  • A list of problems you intend to come back to

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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