How to solve Kakuro

Fill the white cells with digits from 1 to 9 so that each run of cells — across or down — adds up to the number at its head.

A clue cell is cut by a diagonal: the number above it is the sum of the cells to its right, the number below it the sum of the cells beneath.

Within one run no digit appears twice.

Tap a white cell and pick a digit on the pad under the board; the same digit again clears it. With notes on, digits are pencilled small in the cell instead.

A reddish cell holds a digit its run already has, or sits in a run whose sum has gone wrong; a sum greys out once its run is done.

The sums are given at the start and stay put; every white cell is yours to fill. Every board has exactly one solution and can be reached without guessing — when nothing seems to give, there is always some run with only one way left.

A sum can usually be made from different digits in several ways — but the extreme ones in only one. Two cells give at least 3 (1 + 2) and at most 17 (8 + 9); three cells at least 6 and at most 24. Such a run says at once which digits stand in it, though not yet where.

Every white cell lies in a row and in a column at once, so its digit has to fit both sums. Where two runs of sure digits cross, the cell they share usually has only one way out — and that is the most common move in Kakuro.

When a run is missing just one cell, no combinations are needed — subtraction is enough. Towards the end of a board almost every digit written closes some run, and then the board solves itself.

A long run with an ordinary sum has many combinations and says nothing on its own. But its cells lie in other runs too, and those have usually left each cell only a couple of possibilities. Then it pays to go through the run’s combinations one by one and keep only those that can be laid out over those cells.

Sometimes a few rows cover exactly the same cells as a few columns — with one cell to spare. Then the rows’ total and the columns’ total differ by precisely that one cell, and its digit can be worked out without knowing anything about the others. On big boards this is sometimes the only way on.