Powers of Two
Merge adjacent equal numbers to create larger and larger powers of two.
In each turn, move the tiles in one of the four directions. All tiles move simultaneously, and they move as far as possible until they hit the edge of the board or another tile. If two tiles with equal numbers collide, they merge into one tile, and it will have the sum of the two merged numbers. (If more tiles with equal numbers collide, they merge in pairs, starting from the opposite edge to the moving direction. Newly merged tiles cannot merge again in the same turn.) Each merge earns as many points as the value of the newly created tile.
After each legal move, i.e. which moved at least one tile, a random new tile appears on the board with the value 1 or 2 (by default, but it can be changed in the Settings). If the board is full, and there are no more legal moves, the game ends.
Since only equal numbers can be combined, and always two at a time, all numbers will be powers of two (1, 2, 4, 8, 16, ...).
This game is based on the well-known game "2048", generalizing it further. The rules of 2048 can be achieved by setting the possible values of the new tiles to 2 or 4. The default is half of that (1 or 2), which means that the tile 1024 here corresponds to the tile 2048 there, in terms of difficulty.
Keyboard control: move the tiles by arrow keys.
Touch control: swipe the board in one of the four directions.
Mouse control: click on the board near one of the four edges to move the tiles in that direction.