Mathturion

The Square of the Nine Tokens

“Let there be a tablet divided into nine equal cells, three by three. Upon it are placed eight numbered tokens, marked from one to eight, and one empty cell, which is reckoned as nought. A token may be moved only by sliding it into the neighbouring empty cell, as a soldier steps into an open rank.”

By sliding the tokens one at a time into the empty place, arrange the tablet so that every row and every column bears an equal sum — the empty cell counted as nought. This is not the common magic square: the diagonals are of no concern. The horizontal and vertical lines alone must be brought into agreement.

The running sum of each row is shown to its right, and of each column below it. When all six fall into balance, they turn green and the square is solved.

Choose your Mode. In Hard, a token may move only by sliding into the neighbouring empty cell, as the classic puzzle demands — and Best shows the fewest slides in which this particular tablet can be solved. In Easy, you may swap any two cells (the empty one included); there is no shortest-path challenge, so Best is hidden.

Hard: click, tap, or drag a token next to the empty cell to slide it. Easy: tap one cell then another to swap them, or drag one onto another. Reset returns the tablet to how it began; Play Another deals a fresh tablet at any time (it asks before discarding a game in progress). Once solved, use Play Again (same tablet) or New Board (a fresh one).