Kakuro solving techniques

Unique sumstier 1

When: Some sums can be made only one way (3 in two cells is 1+2); the run takes exactly those digits.

Some sums have one combination only: 3 and 4 in two cells, 16 and 17 in two cells, 6 and 7 or 23 and 24 in three, and so on up to 45 in nine. The cells of such a run take exactly those digits, in some order.

From one of our puzzles (7x7): 4 in 2 cells can only be made as 1+3, so B2, C2 use just those digits.

Practise it: Kakuro puzzles at Easy

Last cell of a runtier 1

When: When every other cell of a run is known, the last one is the sum minus the rest.

When all but one cell of a run are filled, the last one is the clue minus the others. It sounds trivial; in a long chain it is what finishes most grids.

From one of our puzzles (7x7): The other cells of the down 12 at B2 add up to 3, so B3 is 12 - 3 = 9.

Practise it: Kakuro puzzles at Easy

Naked singletier 1

When: A cell with one possible digit takes it; the digit leaves both of its runs.

A cell with one candidate left takes it, and that digit leaves both of its runs.

From one of our puzzles (7x7): B2 can only be 3, so neither of its runs uses 3 again.

Practise it: Kakuro puzzles at Easy

Combination intersectiontier 1

When: A cell takes only digits that appear in some combination of its across run and of its down run.

A cell must take a digit that fits both its across run and its down run. List the combinations each run can still make and keep only the digits that appear on both sides.

From one of our puzzles (7x7): The down 12 at B2 in 2 cells can still be 3+9, 4+8, 5+7; B2, B3 lose the digits none of them uses.

Practise it: Kakuro puzzles at Easy

One place lefttier 2

When: A digit every combination of a run needs, with a single possible cell, goes there.

If every combination a run can still make contains a 9, and only one cell of the run can take a 9, it goes there.

From one of our puzzles (8x8): Every combination left for the down 11 at G2 (1+2+3+5) needs a 5, and only G5 can take it.

Practise it: Kakuro puzzles at Medium

Naked pairtier 2

When: Two cells of a run with the same two candidates own those digits.

Two cells of a run that can only be the same two digits own those digits; the rest of the run cannot use them.

From one of our puzzles (8x8): B7 and E7 share the across 30 at B7 and can only be 8 or 9, so the rest of the run cannot.

Full run analysistier 3

When: Try the combinations cell by cell; a digit that fits no complete arrangement is out.

Some combinations look possible but cannot be arranged in the cells you have: a digit fits no cell of the run once the crossings are counted. Work the run cell by cell and drop the digits that never fit.

From one of our puzzles (7x7): Placing the digits of the down 13 at B6 cell by cell, with the candidates each cell has left, only 6+7, 5+8, 4+9 can be completed; B7 loses the digits that never fit.

Practise it: Kakuro puzzles at Hard

Contradictiontier 4

When: If a digit in a cell leads to a broken run a few steps later, that digit is out.

Assume a digit and follow the sums. If a run can no longer reach its clue, the digit is out. Only Expert grids need it.

From one of our puzzles (8x8): Suppose G4 were 1: following the rules from there, the across 3 at G3 would repeat 2. So G4 is not 1.

Practise it: Kakuro puzzles at Expert