Kakuro notation
The app, the technique guides and this page all use the same short notation. It is worth five minutes.
Cells
A cell is named by its row and its column: r2c3 is the cell in row 2, column 3. Rows count from the top, columns from the left, both starting at 1. A list of cells is written r2c3, r2c4.
Runs
A run is a line of white cells with one clue. Runs are named by direction, sum and span:
Across 16 (r2c2-r2c3): the run to the right of a clue that sums to 16.Down 7 (r2c1-r4c1): the run below a clue that sums to 7.
A short form is used in some explanations: 16→r2c1 means "the across run of 16 that starts after the clue at r2c1".
Digit sets
A set of digits is written with braces: {7,9} is the pair 7 and 9, in either order. A single digit is written plainly: 7.
A placement is written 7r2c3: the digit 7 goes in cell r2c3. A removal is written the same way in the app's explanations: if the app says "7 cannot be in r2c3", it has crossed 7 out of that cell.
Pencil marks
The small digits inside an empty cell are pencil marks: the digits that cell can still hold. Placing a digit removes it from every other cell of the same run.
Partitions
A partition is a set of different digits that adds up to a sum. "17 in 2" means a run of two cells summing to 17; its only partition is {8,9}. The cheat sheet lists every partition.