Kakuro
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Tap a square, then a number
Tap a square, then a number
Every run of white squares has a clue at its head: the number above the diagonal is the sum of the run going right, and the number below it is the sum going down. Fill the run with digits one to nine that add up to that total, and no digit may repeat within a single run, though the same digit can appear twice in a row if it belongs to different runs. Tap a square and then a number to enter it. Each puzzle here has exactly one solution.
Kakuro is sometimes described as a crossword with sums instead of words, and the comparison is exact: the clues are numbers, the answers are digits, and every white square belongs to one across run and one down run. Because a run cannot repeat a digit and uses only 1 to 9, most clues have very few possible digit sets. A two cell run summing to 3 is 1 and 2 in some order. A two cell run summing to 17 is 8 and 9. A three cell run summing to 6 is 1, 2 and 3. Solvers memorise these, and the game is largely about spotting them.
Every puzzle here is generated and then checked for a unique solution by a solver that enumerates exactly those digit sets, so there is never a second valid filling. The 7x7 board is built whole. The 9x9 and 11x11 boards are grown from a finished 7x7, a domino or a 2x2 block at a time, and the whole board is checked for a single solution again after every addition, so the guarantee holds at every size.
Not within a single run. The same digit can appear twice in the same row if the two squares belong to different runs separated by a black cell.
Yes. A solver checks each generated puzzle and any with a second valid filling is discarded.
The ones with a single possible digit set: low sums in long runs, high sums in short ones. A two cell 3 or 17 is the classic opening.
-FAQ