Unblock

Solve it backwards

The instinct in Unblock is to start shoving whatever piece your hand lands on. Resist it. The faster method is to work backwards from the exit. Look at the target block, trace the straight lane it needs to reach the edge, and find the one or two pieces sitting in that lane. Those pieces are the puzzle. Everything else on the board matters only if it stops them from clearing.

So the solve becomes a chain of questions. What blocks the target? Say a vertical piece parked across its row. What does that piece need to slide clear: space above, or space below? And what's squatting in that space? Follow the chain two or three links deep and the answer arrives as a sequence, not a scramble.

A jam, worked through

Here's the shape of a typical solve. The target needs to travel right, but a vertical three-long piece stands in its lane. That piece can only move up or down, and up is blocked by the wall, so it must drop two squares. One of those squares is free; the other is held by a horizontal piece. That piece can slide left into an open corner. Now read the answer backwards: horizontal piece left, tall piece down two, target across and out. Three sentences of thinking, half a dozen moves, no shoving. Nearly every board in the game reduces to a chain like this. The hard ones just make the chain longer and loop it through more pieces.

Watch the gaps, not the blocks

A packed board might hold only three or four empty squares, and every move you make simply slides a gap from one side of a piece to the other. That's a useful way to see the game. Ask where the empty squares have to be for the chain to work: the blocker needs two free squares below it, so which piece is sitting on them, and where would that piece push its own gap? Plans built on gaps come out shorter and cleaner than plans built on pieces, because gaps are scarce.

The same view tells you which pieces to even consider. A piece with no empty square anywhere in its lane is frozen: it cannot move this turn no matter how much you want it to. Frozen pieces are scenery until something in their lane shifts, so skip them when planning. The live pieces, the ones that could actually slide right now, are usually only three or four, and your next move is always one of them. That single observation shrinks most boards from a dozen options to a handful.

Three habits cause most wasted moves. Shuffling the same two pieces back and forth while hoping (if a piece isn't in the chain of blockers, moving it does nothing). Advancing the target early, before its lane is fully clear, so it plugs the crossing lanes other pieces still need. And moving without a reason: if you can't say how a move helps the target, don't make it.

• The pieces never rotate. Horizontal slides sideways, vertical slides up and down, forever.
• A piece one square from where you need it can still be impossible to move. What matters is its lane, not the gap you wish it could reach.
• Undo freely. The move counter rewards clean solutions, and a false start you abandon costs nothing but pride.

Nob's traffic jam

The board has a famous family tree. Sliding puzzles first gripped the public in 1880, when the fifteen puzzle, that little frame of numbered tiles, became a genuine craze on two continents. A century later the Japanese inventor Nob Yoshigahara (1936 to 2004), one of the great puzzle designers, refined the idea into this traffic jam, and in 1996 it reached the world as Rush Hour, with the target piece painted as a red car escaping a gridlocked lot. It endures because it scales so cleanly. The same rules make boards a child clears in three moves and boards that demand real planning: when researchers ran every possible starting layout of the classic six-by-six game through a computer, the hardest one they found needs 93 moves. Mathematicians have since shown puzzles of this family are deeply hard in a formal sense, which is worth remembering the next time a small grid of blocks makes you feel slow. It isn't you. It's the math.