Maple Lane school carpool

Why the rules as written fail

Every run carries at least 5 kids, always including Ben and Fay, who each need a booster seat. So the cars on a run need at least 5 kid seats and 2 booster seats.

So all 20 runs (2 weeks x 5 days x 2 runs) need the Abara minivan or the Delgado wagon: Abara + Delgado trips must be at least 20.

The fairness rule caps each family at 8 trips, so Abara + Delgado trips can be at most 8 + 8 = 16. Twenty runs cannot fit in sixteen trips, so no schedule follows every rule (rules 1, 2, 3, 4 and 5 clash). A full computer search (solve.py) confirms it.

Fix 1: raise the fairness maximum from 8 to 10 (10 + 10 = 20; 9 would give only 18).
Fix 2: install 1 booster seat in the Chen SUV. Brooks + Chen then has 8 seats and 2 boosters, so the 4 Tuesday and Thursday afternoons no longer need Abara or Delgado, leaving 16 runs for 8 + 8 trips.