Why a school bus?

A traffic-jam puzzle always has one vehicle that needs to get out. Here it is a yellow school bus with three kids waving from the windows. It is stuck in the car park next to the school, and every car and truck around it is in the way.

The twist is the clock on the school. It starts as many minutes before the bell as the fewest moves the puzzle needs, and every slide moves it on by one minute. Find the shortest way out and the bus rolls through the gate just as the bell rings. Take a longer way and you get in a few minutes after it, which is fine. The clock never ticks by itself, so there is no rush. When the bus gets out, the kids cheer.

A bit of real sliding-block history

Sliding puzzles are older than cars. The 15 puzzle, with numbered tiles in a box and one empty space, was invented by Noyes Palmer Chapman, a postmaster in Canastota, New York. It became a craze in the United States in 1880.

Puzzles with blocks of different sizes came next. In 1909 Lewis W. Hardy copyrighted the Pennant Puzzle, where one big block has to work its way past smaller ones to the far end of a tray. A Chinese version called Huarong Dao takes its story from the novel Romance of the Three Kingdoms. In February 1964 Martin Gardner printed an 81-move solution to this kind of puzzle in Scientific American.

The traffic version came from Nob Yoshigahara, a Japanese puzzle inventor, in the 1970s. Cars and trucks sit on a 6 by 6 grid and can only drive forward and back. In 1996 the American company Binary Arts, now called ThinkFun, started selling it as Rush Hour with 40 puzzle cards, and it sold more than a million copies.

Computer scientists got interested too. In 2002 Gary Flake and Eric Baum proved that the puzzle, played on bigger and bigger boards, belongs to a group of very hard problems called PSPACE-complete. In 2018 the software developer Michael Fogleman used a computer to search the 6 by 6 board. The hardest layout he found with no walls needs 51 moves, counting a slide of any length as one move. This game counts moves the same way.

The four car parks

All 60 levels were checked by a computer search, so the number under each level is the true fewest moves.

• Beginner, levels 1 to 15: 2 to 9 moves, with only a few cars at the start.
• Intermediate, levels 16 to 30: 10 to 17 moves and a fuller car park.
• Advanced, levels 31 to 45: 18 to 28 moves. Expect to move some cars twice.
• Expert, levels 46 to 60: 29 to 49 moves. The last one is the hardest layout we found.

How to play

• Cars are 2 spaces long and trucks are 3. Each one slides forward and back along its own lane and never turns.
• Drag a vehicle to slide it, or tap it and then tap an empty space in its lane.
• Get the yellow school bus out through the gate on the right of its row.
• One move is one slide of one vehicle, however far it goes.
• On a keyboard, Tab picks a vehicle, the arrow keys slide it, and Backspace undoes a move.
• Hint shows the next move on a shortest route. Using one means 2 stars at most for that level.
• Stars: 3 for the fewest moves with no hint, 2 for up to 3 extra moves, 1 for any way out.
• Earn 3 stickers in this game for your QuickBOP sticker book.

Tips

Start from the bus. Look along the bus’s row to the gate and find every vehicle standing in it. Those are the blockers.

Count the blockers. Each blocker needs at least one move, and the bus needs one more at the end. Two blockers means at least three moves. If the fewest is much bigger than that, one of the blockers is blocked too.

Work backwards. Pick a blocker and ask which way it has to go to clear the bus’s row, then ask what is stopping it. Keep asking until you reach a vehicle that can move right now. That is your first move.

Trucks go down. There are only two spaces above the bus’s row, so a truck standing across it can only clear the way by going all the way down. Make room under it early.

Undo is free. Only the moves you keep count toward your stars, so try an idea and take it back as often as you like.

Your turn

The bus at the top of this page has one car in its way and the bell two minutes off. Clear the road and listen for the cheer.