How to play Unjam

Unjam is a sliding-block puzzle, and it is the rare kind where the target score is not a designer's opinion. Everything below follows from two facts: blocks cannot turn, and par is proven.

The rule

The tray is six squares by six. Each block covers two or three squares and lies either upright or flat. A block slides only along its own length — upright blocks up and down, flat blocks left and right — and it can never rotate, so a block's lane is fixed for the whole puzzle. Blocks stop against one another and against the walls.

Only the red block ever leaves, through the gap in the right-hand wall on its row. Everything else exists to be shuffled out of its way.

What counts as a move

One move is one block shifted any distance in one direction. Sliding a block a single square and sliding it four squares both cost exactly one. This matters more than it sounds: the cheapest-looking route is often the one that nudges a block twice when a single longer slide would have done, and the difference between a good solve and a par solve is frequently three or four moves of exactly that kind.

Par is not an estimate

Before any tray shipped, a breadth-first search explored the puzzle exhaustively and found the shortest solution that exists. That number is the par. It is not a target the designer felt was fair, and it is not the length of some particular solution somebody happened to find — it is the proven minimum.

Two things follow. First, you can never beat par: if the display says 23, then 22 is impossible, and a search that examined every reachable arrangement says so. Second, matching par is a real achievement rather than a participation mark. Most solvers land four to ten moves over on a hard tray, and closing that gap is the whole game.

How to think about it

The temptation is to grab the red block and shove it right. That is almost never the first move, and on a hard tray it is often a wasted one.

Work backwards instead. Look at what is directly blocking the red block's row and ask what would have to move for that blocker to get out of the row. Usually it cannot move yet, because something is under or over it — so ask the same question about that one. Two or three steps of this and you find the block that actually can move right now, and it is frequently nowhere near the red one.

The second habit worth building is noticing which blocks have no room at all. A tray usually has three or four blocks that are completely wedged at the start. They are not part of the puzzle yet, and time spent staring at them is wasted; the action is in the two or three blocks with a square of slack.

Hints, undo and reset

A hint runs a fresh search from your current position — not from the start — and shows the single best move from exactly where you are. This is deliberate. A stored solution would be useless the moment you left it, which is most of the time. Because the search is live, the hint is just as valid twenty moves into a mess as it is on the first move, and it will also tell you how many moves remain from where you stand, which is the honest measure of whether your last idea helped.

Undo steps back one move and lowers your count again, so exploring costs nothing but time. Reset returns the tray to its opening position with the counter back to zero.

The daily tray

One tray per day, the same for everybody. The week ramps: Monday and Tuesday are easy, Wednesday and Thursday medium, Friday and Saturday hard, and Sunday is an expert tray. Solving it extends your streak, solves at exactly par are counted separately, and the share text carries your moves against par without revealing anything about the tray.