How to Solve Killer Sudoku: A Step-by-Step Guide for Beginners

If you can solve a regular sudoku, you can solve a killer sudoku — you just need to learn one new habit: turning cage sums into digits. This step-by-step guide walks a complete beginner through that first solve, from reading the dotted cages to filling in your opening cells with confidence. There's no hard math here, just small addition and the same one-of-each logic you already know. Let's solve your first killer sudoku together.

For the formal rulebook, the killer sudoku rules page covers every edge case. This guide is the friendly version that gets you playing.

What you're looking at

A killer sudoku is a normal 9x9 sudoku grid with two changes. First, there are usually no given numbers at all. Second, the grid is divided into dotted-outline groups called cages, and each cage has a small number printed in its top-left corner — that's the sum of the digits inside it.

Three rules apply at the same time:

• Every row, column, and 3x3 box holds 1 to 9 with no repeats (standard sudoku).
• The digits in each cage add up to the cage's printed sum.
• No digit repeats inside a cage.

That third rule is the one beginners forget, and it's doing more work than you'd think.

Step 1: Read the smallest cages first

Your opening move is to find cages where the sum forces the digits. Small two-cell and three-cell cages with extreme sums are the easiest.

• A two-cell cage summing to 3 must be 1 and 2. Nothing else adds to 3 with two different digits.
• A two-cell cage summing to 17 must be 8 and 9.
• A three-cell cage summing to 6 must be 1, 2, and 3.
• A three-cell cage summing to 24 must be 7, 8, and 9.

When you find one of these, you don't know which cell gets which digit yet — but you know exactly which digits live there. Pencil them in lightly as a pair or trio. That's real progress on a board that started completely blank.

Step 2: Use the 45 rule for a free digit

Here's the move that feels like magic the first time. Every 3x3 box contains 1 through 9, so every box adds up to 45. The same is true of every row and every column.

Find a box where the cages are almost entirely inside it. Add up those cage sums. If they come to 41 and there's one lone cell that belongs to a cage spilling outside the box, that cell must be 45 − 41 = 4. You just placed a digit with arithmetic alone, no candidate hunting required. This is the famous 45 rule, and it's the beginner's best friend on hard grids.

Step 3: Cross cages against the grid

Most cages have more than one possible combination. The way forward is to use what you've already placed to rule options out.

Picture a three-cell cage summing to 8. The options are {1,2,5} and {1,3,4}. Now suppose the row through one of those cells already contains a 5 somewhere outside the cage. The {1,2,5} option needs a 5 in the cage, but it can't sit in that row — and if the cage geometry forces it there, {1,2,5} is dead. You're left with {1,3,4}. Each digit you place sharpens the next cage.

Step 4: A full worked example

Let's solve a corner. Say the top-left box has these cages: a two-cell cage summing to 4, a two-cell cage summing to 17, and a five-cell cage summing to 24.

• The 17 cage is locked: it's {8,9}.
• The 4 cage is locked: it's {1,3}.
• That accounts for four cells holding {1,3,8,9}. The box must total 45, and these four cells contribute 4 + 17 = 21. So the remaining five cells of the box hold 45 − 21 = 24 — which matches the five-cell cage's printed sum. Good, the box is consistent.
• The five-cell cage summing to 24 can't use 1, 3, 8, or 9 (they're already claimed by the box), so it's drawn from {2,4,5,6,7}. And 2+4+5+6+7 = 24 exactly. That means the five-cell cage is all five of those digits — a fully locked cage.

In a few lines of reasoning we've pinned down every digit in the box; only their exact positions remain, and the row and column constraints settle those. That's a complete killer sudoku solve in miniature.

Step 5: When you get stuck

Every beginner hits a wall where nothing jumps out. The fixes, in order:

• Re-check the 45 rule on every row, column, and box. You almost certainly skipped one that's nearly complete.
• Write full candidate lists. Once the obvious cages are placed, slow down and note every possible digit for each empty cell. Seeing the options written out reveals hidden singles and pairs you can't hold in your head.
• Look for a cage you haven't filtered. A cage with three combinations often drops to one after you re-read its row and column.

And never guess. Our puzzles always have exactly one logical solution. A coin-flip feeling means there's a deduction waiting, not that the puzzle is broken.

Where to play your first one

Open an easy killer sudoku — these start with 20 to 30 given digits and small cages, so the locked-cage technique alone will carry you a long way. When easy feels comfortable, the full killer sudoku strategy guide shows you every technique in the order you'll need it. Prefer paper? Grab a printable killer sudoku.

The best way to learn how to solve killer sudoku is to solve one. Find a locked cage, place your first pair, and go.

Frequently asked questions

How do you start a killer sudoku with no given numbers?

Start with the smallest cages that have only one possible combination — like a two-cell cage summing to 17, which must be 8 and 9. Then apply the 45 rule to any box that's nearly filled with cages to pull out a free digit. Those two moves give you a foothold on a blank grid.

Is killer sudoku harder than regular sudoku?

For a beginner, yes, mostly because the blank grid looks daunting and you have to learn cage logic. But once the locked-cage and 45-rule habits click, many solvers find killer sudoku more satisfying because the cage sums give you extra ways in. See killer sudoku vs regular sudoku.

What is the secret to killer sudoku?

There's no single secret, but the closest thing is the 45 rule: every row, column, and box sums to 45, which lets you deduce single cells by subtraction. Combine that with memorizing the locked cage combinations and most puzzles open up.

Do cages have to be next to their number?

The sum is printed in the top-left cell of the cage, and the cage is the group of cells joined by the dotted outline. The digits can sit in any arrangement within that outline, as long as they add to the sum and don't repeat.

Can a digit repeat in a killer sudoku cage?

No. Digits never repeat inside a single cage, even when the sum would mathematically allow it. A four-cell cage summing to 14 cannot be {2,2,4,6} — every digit in a cage must be different.