How to play kakuro

The rules, in about a minute

A kakuro grid is a crossword built out of numbers. There are no word clues. Instead, the dark cells carry small totals in their corners, split by a thin diagonal so you can tell which run each total belongs to:

• The number above the diagonal, in the top right, is the total of the white run running across to its right.
• The number below the diagonal, in the bottom left, is the total of the run heading down beneath it.
• Every white cell takes one digit from 1 to 9. Each run has to hit its total exactly, and no digit may appear twice inside one run. The same digit is free to show up all over the grid. It just cannot sit in the same run twice, the way two cats will happily share a house and not a sunbeam.

That last rule is the whole reason kakuro is a logic puzzle and not an arithmetic quiz. A run of two cells totaling 4 cannot be 2 and 2. It has to be 1 and 3, in some order, and that fact alone is a tool you will use on nearly every board you ever solve.

Your first solve, step by step

Here is about the smallest honest kakuro there is: two across runs, two down runs, four white squares between them. The 4 and the 6 clue the columns. The 3 and the 7 clue the rows. Four digits are going to slot in, and every one of them will be forced.

The starting grid. The columns have to reach 4 and 6, the rows 3 and 7, and nothing is in the box yet.

Step 1: find the tightest clue

Always start where the board has the least room to wriggle. The across 3 is as tight as a clue gets: two different digits adding to 3 can only ever be 1 and 2. You do not yet know which square takes which, so pencil both digits into both squares and leave them to settle.

Step 2: cross it with another run

The down 4 is nearly as tight. Two different digits adding to 4 can only be 1 and 3, because 2 and 2 would be a repeat. Now look at the square where those two runs cross, top left. The across run says it is a 1 or a 2. The down run says it is a 1 or a 3. Only 1 keeps both of them happy, so that square is settled and it never needed a guess. The two clues simply talked each other down until one digit was left standing.

The crossing of 3-across and 4-down can only hold a 1. Placing it strikes the 1 out of the pencilmarks beside it and below it.

Step 3: let the answer ripple

Every digit you place tightens the two runs it sits in, and this is where a solve picks up speed. The across 3 already has its 1, so its other square has to be 2. The down 4 already has its 1, so the square underneath has to be 3. Two more squares, no new arithmetic.

Step 4: check the finish

One square is left, and both of its clues agree about it. The across 7 has a 3 already, so it wants a 4. The down 6 has a 2 already, so it wants a 4 as well. When two runs ask for the same digit in the same square, the grid is telling you it is finished. Pop it in and the board is done.

Solved: 1 + 2 = 3 across, 3 + 4 = 7 across, 1 + 3 = 4 down, 2 + 4 = 6 down.

The habit that carries you

Everything you just did scales. Real boards are bigger and the loop is identical: find the tightest clue on the grid, pencil in the few digits it allows, then walk the crossings, because every square has to satisfy two runs at once and one of them is usually fussier than the other. Do that on repeat and large grids come apart in the same unhurried way this one did.

When you want the patterns that make the big ones fall, the techniques guide is the next stop, and the combinations chart lists every clue's options so you never work one out by hand again.

Learn by solving

Catkuro opens with a twenty-five-chapter teaching ramp that grows from a grid about the size of the one above into full boards, a digit and a row at a time. Start with four feline friends, bring five more home through Act 1, then fill their home with cozy places and favorite things. All 2,000+ puzzles are free, and no ad ever interrupts a solve.