THE IDEA: SUMS WITH NO REPEATS
A Kakuro grid is black clue cells and white answer cells. Every white run — a straight line of white cells going across or down — has a target sum, written in the black cell at its start. The number in the top-right of a split clue cell is the across sum (for the run heading right); the number in the bottom-left is the down sum (for the run heading down.)
Two rules, that's the whole game:
- Each run adds up to its clue. Fill the white cells with digits 1–9 so the run hits its target sum exactly.
- No digit repeats inside a run. A run of two can be 1+3 but never 2+2. (Different runs can reuse digits freely — the no-repeat rule is per-run.)
And the no-repeat rule is the secret: it means short runs often have exactly one possible set of digits. Those are your way in.
LET'S ACTUALLY SOLVE ONE — STEP BY STEP
Here's a real Kakuro. Black cells with little numbers, white cells waiting to be filled. Don't try to take in the whole thing — we only ever look at one short run at a time.
The starting grid — clue sums in the black cells, white cells empty.
Step 1 — find a "magic block": a run with only one possible set.
Look at this little down run of two cells — it's clued 3. What two different digits add to 3? Only 1 and 2. (Not 1+1 — no repeats!) So this pair is a 1 and a 2, in some order. We just don't know which way round yet. These one-and-only-one-set runs are called magic blocks — hunt them first.
Step 2 — cross-reference: the crossing run decides the order.
Now look at the cell where our pair meets an across run (the blue line), clued 4. Two different digits adding to 4? Only 1 and 3. So that shared cell has to be a digit that works for both runs — it's in {1 and 2} and in {1 and 3}. The only number in both lists is 1. Done — that cell is a 1. This is cross-referencing, and it's the heartbeat of Kakuro.
Step 3 — completion: the last cell of a run is forced.
Back to our down pair. It needs to total 3, and one cell is now a 1. So the other must be 2 (1 + 2 = 3). When every cell of a run but one is filled, the last is just clue minus the rest — no thinking required. That's completion, and it's what makes Kakuro cascade.
From here it tumbles. Each digit you place is a known number in a crossing run, which shrinks that run's options, which forces another cell… A couple of magic blocks and cross-references open the door; completion walks you through the rest of the house.
Cascading — the bottom runs fall into place off that first chain. Each filled cell feeds the run that crosses it.
Done. Add up any run — it lands on its clue, every digit different. 👻
THE THREE MOVES, IN ORDER
Almost every easy Kakuro falls to the same little loop:
- Magic block → write the set. A short run whose sum has only one possible digit-set tells you which digits live there (just not the order yet). Find these first.
- Cross-reference → pin the order. Where two runs cross, the shared cell must work for both. The digit in both runs' sets is forced.
- Completion → finish the run. When a run has one empty cell left, it's just clue minus the rest. These cascade — one fills, the next is forced.
Never a guess: every digit has a sum-sized reason behind it. Stuck on a run? Look at a run that crosses it — the shared cell almost always gives you the next move.
A FEW MAGIC BLOCKS WORTH KNOWING
You don't need to memorise these — but spotting them is a superpower. Each is a run length + sum with exactly one possible set:
- Two cells: 3 = {1, 2} · 4 = {1, 3} · 16 = {7, 9} · 17 = {8, 9}
- Three cells: 6 = {1, 2, 3} · 7 = {1, 2, 4} · 23 = {6, 8, 9} · 24 = {7, 8, 9}
The lowest and highest sums for each run length are always magic — there's only one way to make them. Those are the corners you pry open first.
THAT'S IT — GO DO ONE
Find a magic block, write its digits, let a crossing run pick the order, then complete the runs one by one. The first time a single pinned cell cascades through a corner of the grid, you'll see why people love this one — it's a crossword where the answers are pure logic, no vocabulary, no ads mid-puzzle, just you, some small sums, and a ghost who's quietly chuffed when the last cell lands.