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The fifteen puzzle is a 4x4 grid holding tiles numbered 1 through 15 plus one empty space. Slide a tile adjacent to the blank into the gap to move it. The goal is to arrange all tiles in order from 1 to 15, left to right and top to bottom, with the blank in the bottom-right corner. Only about half of all starting configurations are actually solvable, so the game always begins from a valid scramble.
Work row by row from the top. Place tiles 1 and 2 first, then 3 and 4 together using a rotation technique that avoids breaking earlier placements. Repeat for the second row with tiles 5 through 8. For the final two rows, use column-by-column placement starting from the left. The key is recognizing that inserting one tile in isolation often disrupts neighbors, so learn the small rotation patterns that handle two or three tiles simultaneously.
The fifteen puzzle became a craze in North America and Europe in the early 1880s, reportedly distributed by puzzle entrepreneur Sam Loyd, though historians attribute the invention to Noyes Chapman. Loyd offered a cash prize for solving an unsolvable position, which attracted enormous public attention. Subsequent mathematical analysis proved that exactly half of all permutations are reachable. The puzzle inspired entire fields of study in permutation groups and search algorithms.
The 15 puzzle tracks your Moves counter, and lowering it is the real measure of skill once you can solve reliably. The hardest legal scramble is provably solvable in 80 single-tile slides, so a typical scramble can be cleared in far fewer with planning. Avoid sliding a tile back and forth, which inflates your count without progress. Each useful relocation of a far-off tile takes a fixed cycle of slides around the blank, so memorizing the 3-tile and 2-tile rotation cycles cuts wasted moves dramatically. Before touching a tile, trace mentally where the blank must travel to bring it home. Solving the top two rows and the left two columns first leaves a 2x2 corner that often resolves in one short rotation. Use Shuffle to drill the same techniques repeatedly until the cycles become automatic.
The most frequent error is solving the last two tiles of a row first, which traps you in a position where the final tile cannot enter without disturbing finished tiles. Instead, place the second-to-last and last tile of each row together using a corner-setup rotation. Another mistake is solving rows all the way to the bottom; the final two rows must be solved by columns, not rows, or you will deadlock. Players also forget that only the tile directly beside the empty space can move, so trying to slide a distant tile does nothing. Finally, do not panic when a near-complete board looks scrambled mid-technique; rotation cycles intentionally pass through messy intermediate states before snapping pieces into place. If you truly stall, Shuffle resets to a guaranteed-solvable position.
The game only generates solvable starting positions. In a 4x4 fifteen puzzle exactly half of all permutations are reachable, so a random shuffle could land on an impossible one. The Shuffle button filters those out, guaranteeing the arrangement you see can always be solved.
No. Only a single tile directly next to the empty space slides into it per move, and the counter increases by one each time. Clicking a tile farther from the blank does nothing, so plan the blank's path to bring the tile you want adjacent.
It depends entirely on the scramble. The worst-case position needs 80 moves, but most shuffles solve in 40 to 60 with good technique. Lowering your Moves count means avoiding back-and-forth slides and using efficient rotation cycles to place several tiles per setup.
Stop solving by rows after the top two rows and switch to columns. Solve the leftmost two tiles of both bottom rows together, then the next column pair, working left to right. The final 2x2 corner then rotates into place in one short cycle.
Yes. Shuffle deals a fresh solvable scramble and starts your Moves counter back at zero, while New Game does the same with a new board. Use Shuffle when you want to retry the same techniques without finishing your current attempt.