How to play Fifteen

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Fifteen is the classic sliding-tile puzzle: fifteen numbered plaques in a four-by-four tray with one empty socket. Slide them until they read 1 to 15 in order, with the gap in the bottom-right corner.

The goal

This is the finished board. Everything below is about getting there without going in circles:

The solved position — 1 to 15 in reading order, gap last.

Controls

A plaque can only ever move into the gap, and only from directly beside it — never diagonally, and never more than one at a time. That single restriction is the whole puzzle.

Every board can be solved

Only half of all possible arrangements of a 15-puzzle are actually solvable. The other half are unreachable no matter how well you play — which is the source of a great deal of historical frustration, and of at least one famous 19th-century prize that could never be won.

Fifteen checks the parity of every shuffle before dealing it and only ever hands you a solvable board. If you're stuck, it's the method — not the deal. That's a promise the game makes deliberately, so a hard board is always worth persevering with.

A method that always works

Beginners tend to solve the puzzle by wandering: pushing plaques toward roughly where they belong and hoping. That works until the last few tiles, and then it collapses, because fixing one late tile un-fixes another. The reliable approach is to solve the board in a fixed order and never disturb what's already finished.

1. Top row first, left to right

Place 1, then 2, then 3. Get 4 last. Once the top row is complete, treat it as a wall — the rest of the puzzle happens in the three rows below it, and you never move a top-row plaque again.

2. The corner trick for 4 (and 8)

The end-of-row tile is the one that traps people. Don't try to slot 4 straight into its corner. Instead, put 3 in the corner where 4 belongs, park 4 directly beneath it, and then rotate the pair into place together. The same manoeuvre finishes the second row with 7 and 8.

3. Second row, same way

Now do 5, 6, and then 7-and-8 as a pair. Two rows are now locked and you're working in a four-by-two strip.

4. The last two rows, in columns

Stop thinking in rows here. Solve the bottom two rows column by column: place 9 and 13 together, then 10 and 14 together. That leaves 11, 12, 15 and the gap in a two-by-two square, which resolves with a simple rotation. If it won't resolve, you've accidentally moved a finished tile — back up rather than forcing it.

Getting faster

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