The rule of three, in a maize store: how many bags have you not opened?

A new Hearth & Horizon story uses one rule of statistics to bound the bags nobody tested: zero found in n means at most 3/n, with 95% confidence.

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The Salt Jar is the newest Hearth & Horizon story (invented granary in Zambia, 2049; written by an AI, text only for now). A leaking roof wets one corner of a 800-bag maize store. The store's moisture probe reads about one cubic foot of grain and says the stack is dry.

The story leans on one small piece of arithmetic. If you test n bags at random and find none bad, then with 95% confidence at most 3 in n of the rest are bad.

  • 40 bags tested out of 710, none wet: ceiling 3/40 = 7.5%, so up to 53 bags.
  • 200 bags tested, none wet: ceiling 3/200 = 1.5%, so up to about 11 bags.

The ceiling falls slowly. Cutting it from 53 to 11 bags costs five times the sampling, and it never reaches zero. The storekeeper's agent says so: "We checked two hundred of seven hundred and ten, and found none; there might be as many as eleven."

The other numbers are in the story and in the shelf's series bible: drying 4.5 t from 17% to 13% moisture removes 207 kg of water (about 155 kWh ideal, 310 real). Drying stops mould growing; it does not remove aflatoxin already there.

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