35 puzzle · 6×6 board
Thirty-five tiles. The long, meditative one.
Tap or drag a tile next to the empty space to slide it. Arrow keys work too. Every shuffle is solvable.
By hand, usually 10 to 25 minutes and 300 to 600 moves, depending on how strictly you follow the layered method. The optimal solution for a hard position is unknown; the board has 36!/2 solvable positions, roughly 1.9 × 10⁴¹, and no computer search has come close to exhausting it.
Exactly like a smaller one, just more times. Solve the top row and lock it, solve the left column and lock it, and you have a 5×5 puzzle. Repeat to 4×4, then 3×3, then finish the last 2×2 corner by rotation. Never move a tile out of a finished row or column.
Exactly half of all arrangements can. Because the board width is even, the test is: count the inversions in reading order and add the row of the empty cell counted from the bottom, starting at 1. The position is solvable when the total is odd. Every board on this page is shuffled by legal moves, so it always passes.