A Beginner's Guide to Kakuro: Rules, Strategy, and Your First Solve

A clue cell shows a 4 in its upper-right triangle, and the run of white cells to its right is two cells long. That is almost enough to fill it: you need two different digits from 1 to 9 that add to 4, and the only pair that works is 1 and 3. You do not yet know the order, but you have already cut the run down to two possibilities. That is Kakuro in miniature — small sums, distinct digits, and combinations that give themselves away.

Kakuro looks like a crossword crossed with arithmetic, and that is exactly what it is. If you can add to single digits and notice when a sum can only be made one way, you can solve one. Here is everything you need for a first board.

How a Kakuro grid is laid out

The grid mixes white cells you fill with shaded clue cells you do not. A shaded cell can carry two numbers split by a diagonal: the number above the diagonal is the sum for the run of white cells going right; the number below is the sum for the run going down. A "run" is just an unbroken line of white cells between clue cells. Every white cell belongs to exactly one across-run and one down-run, which is what makes the puzzle interlock.

The one rule that drives everything

Within a single run, the digits must all be different. A run summing to 10 across three cells could be 1+2+7 or 1+4+5 and several others, but never 2+2+6, because the 2 repeats. That no-repeats rule is what turns sums into logic: it sharply limits which digit sets can fill a run. The same digit can still appear in a crossing run, which is how the across and down constraints together squeeze each cell.

Your first solve, step by step

Start by hunting the runs that can be filled only one way — short runs with extreme sums. A two-cell run of 3 is {1,2}; of 4 is {1,3}; of 16 is {7,9}; of 17 is {8,9}. Place each forced set wherever it lands. Then use the crossings: if an across-run says a cell is a 1 or a 3, and the down-run through that same cell says it is a 7 or a 9, there is no overlap, so you have misread a clue. When the two runs share exactly one possible digit, that cell is solved — and solving it usually forces its neighbours.

Lean on combinations

The fastest Kakuro solvers recognise forced combinations on sight, the way chess players see familiar positions. You do not have to memorise a table — just notice that the smallest sums force the smallest digits and the largest force the largest. Sukuro can list every valid combination for a selected run, so early on you can spend your attention on the cross-referencing rather than the arithmetic.

Common beginner mistakes

• Repeating a digit within a run — legal-looking sums like 2+2+6 are not allowed; the digits in a run must differ.
• Mixing up which clue belongs to which direction — the upper number is the across (rightward) sum, the lower is the down sum.
• Filling a long run too early — start with short, forced runs and let their digits constrain the longer ones.

Across and down are one puzzle

The reason Kakuro is solvable at all is that every white cell answers to two clues at once — its across-run and its down-run. A digit you cannot pin down from the across sum alone often becomes obvious the moment you check the crossing down sum, and the other way around. Treat the two directions as a single combined constraint on each cell rather than two separate puzzles, and the grid stops feeling like arithmetic and starts feeling like logic.

Practice it now

Open a small Kakuro and, at first, do nothing but find every two- and three-cell run with a forced combination. Place those, follow the crossings outward, and watch the board cascade. Once the single-combination runs feel automatic, step up the size and let the combination assist fade into the background.