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One washer, one dryer, one pile of loads. Pick the washing order that gets the last load out of the dryer soonest.
Every load has to be washed first and dried after, and there is only one of each machine. The washer starts the next load the moment it is free, but the dryer can only take a load once that load is out of the washer — so while it waits, the dryer stands idle. The only thing you control is the order.
Tap the loads in the order you want them washed and the two rows fill in: the top row is the washer, the bottom row the dryer, and the gaps in the bottom row are the time the dryer spends doing nothing. The big number is when the last load finally comes out. Tap a load again to pull it back out of the queue.
Press run when you are happy with the order. Match the shortest finish that exists for that pile and the round is yours. Miss it and you lose a heart, and the best order is shown to you so you can see where the time went.
Every three rounds another load joins the pile. Three misses ends the run, and so does the clock. Your score is the number of rounds you clear.
This is a two-machine flow shop, one of the few scheduling problems where the exact best answer is not just findable but findable by hand. The rule is Johnson's rule, from 1954, and it is short enough to memorise. Split the loads into two groups: those whose wash time is shorter than or equal to their dry time, and those whose wash time is longer. Run the first group first, ordered by wash time from shortest to longest. Then run the second group, ordered by dry time from longest to shortest — so the load with the longest dry ends up as late as possible, and the one with the shortest dry finishes the day.
The reason it works is easier to feel than to prove. The dryer is the machine that ends the day, so the whole aim is to have something waiting for it as early as possible and as little as possible left for it at the end. A load with a quick wash and a slow dry is perfect to start with: it clears the washer almost immediately and the dryer gets going while the washer is still busy. A load with a slow wash and a quick dry is perfect to end with: nobody is waiting behind it, and once it finally reaches the dryer it is gone in moments. Everything in between sorts itself out from those two ends.
The measurements say how much the rule is worth. Across thousands of randomly generated piles, Johnson's order hits the shortest possible finish 100% of the time — that is not a statistic, it is the theorem. Learning only half the rule and sorting purely by wash time gets there about 48% of the time. Washing them in the order they happen to appear gets about 10%, roughly the same as shuffling them at random.
The trap worth naming is the greedy move: at each step, add whichever load pushes the finish time out the least. It feels like the careful thing to do and it is the worst policy measured here, hitting the best finish only about 4% of the time — noticeably worse than random. It fails because early on almost nothing changes the finish time, so it picks by a tie-break that means nothing, and by the time its choices matter the good loads for the ending have already been spent. Sort by the rule instead of searching one step at a time.