Holding a rule instead

One caretaker checks a school's water tank. Two guessers try to answer for her. Should she call the water tanker today?

A tanker is a truck that brings water. Today the gauge reads 6, which means 6 steps below full. It has been 0 days since the last fill. Each learned day has a word, call or wait.

The rule

The pile says call. The rule says wait. On that real day the caretaker called. So the pile was right.

One guesser keeps the examples and one keeps a rule of numbers. Each answers the same stated day from what it kept.

• The pile — keeps its eight learned days. It finds the nearest day, the one closest in gauge and days. It answers with that day's word.
• The rule — two numbers, called weights, and a threshold, one fixed number. It keeps nothing else. Here the threshold is 40. A total of 40 or more says call.

A weight is not how heavy anything is. It is how much attention an input gets. A bigger weight means that input counts for more. The gauge gets weight 6. The days since the last fill get weight 4. That is the whole machine. No pile of days is stored behind it.

Both guessers can answer for any gauge reading and any day count. The board shows every pair of gauge and days. Gauge runs from 0 to 8. Days run from 0 to 6. That gives 9 × 7 = 63 days. On the 63 days of the board, they agree on 59. On the day above, they do not.

Slide the gauge and the days below. Find a day where the guessers disagree.