Kakuro is a number crossword. Instead of words you write digits, and instead of definitions every run of squares has a sum. It uses simple arithmetic, but the real skill is knowing which sets of digits can make each sum.
The rules
The grid has dark clue squares and white squares. A run is a line of white squares across or down.
Each clue square is split corner to corner: the number in the top-right is the sum of the run to its right, and the number in the bottom-left is the sum of the run below it.
Fill every white square with a digit from 1 to 9 so each run adds up to its clue.
A digit can appear only once in a run, so 4 in two squares is 1+3, never 2+2.
Every puzzle has exactly one solution.
Playing on Everyday Games
Tap a white square, then tap a digit on the number pad. On a computer you can type digits and move with the arrow keys.
The selected square’s runs are shaded, and a helper under the board lists the digit sets that can make each one, like “17 in 2: 8+9”. Sets that don’t include digits you’ve already placed are left out.
Turn on Notes to pencil in candidates. Placing a digit clears it from the notes in the same runs.
Repeated digits turn red, and so does a clue whose run adds up to too much or to the wrong total once it’s full.
Choose Easy (6×6), Normal (8×8) or Hard (10×10). Your best time is kept for each.
Combinations worth knowing
Some sums can only be made one way, and they are the best places to start. In two squares, 3 is 1+2, 4 is 1+3, 16 is 7+9 and 17 is 8+9. In three squares, 6 is 1+2+3, 7 is 1+2+4, 23 is 6+8+9 and 24 is 7+8+9. In four squares, 10 is 1+2+3+4 and 30 is 6+7+8+9.
The smallest and largest sums for a length are always single combinations, so watch for clues near either end.
Solving tips
Cross the runs: a square belongs to one across run and one down run, so it can only hold digits allowed by both.
If a run must contain a digit (say a 9) and only one of its squares can take it, that’s where it goes.
In a two-square run, once one digit is placed the other is fixed: it’s the clue minus the first.
Use notes for squares down to two or three candidates, then look for the run that settles them.
Nearly finished runs are easy wins: the last empty square is the clue minus the digits already there.
Difficulty levels
Easy and Normal puzzles can always be solved by reasoning about each run’s possible combinations, with no guessing. Hard puzzles are bigger, with longer runs, and sometimes need you to follow a chain of consequences across several runs. Every puzzle is freshly made and checked to have exactly one solution, and a few digits are filled in from the start when that’s needed to make it unique.