Killer Sudoku Tips and Strategies: What to Try, and When

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Published May 8, 2026 · Updated October 16, 2026

Most killer sudoku advice is a list of techniques. The harder question is which one to try next when the grid stops moving, and how far each level of puzzle will push you. We answered it by measurement. Our own solver works through a killer the way a careful person does, always taking the easiest move that makes progress, and we ran it over 1,200 boards from the generator behind our Killer Sudoku game, 300 at each level. Then we switched techniques off one at a time to see which boards could still be finished.

This guide is the result: the order, what each level needs, and one real Hard board followed from its first digit to its last. If you are new to cages and totals, our rules of Killer Sudoku guide starts at the beginning.

What order should you solve a killer sudoku in?

Easiest first, and back to the top after every success. This is the ladder our solver climbs, one rung at a time:

1. Cage arithmetic. Keep only the digits that some set of different digits reaching the cage’s total allows; a one-cell cage simply is its total. Our Killer Sudoku combinations chart lists every set. It was our solver’s first move on every board it finished.
2. Singles. A cell down to one candidate, or a digit that fits in only one cell of its row, column or box: naked singles and hidden singles.
3. Confined digits. When every possible set of a cage needs some digit, and the cage’s cells that can take it all share a row, column or box, that digit leaves the rest of the house. Plain locked candidates sit on the same rung.
4. Pairs and triples: naked pairs, hidden pairs and naked triples, exactly as in classic sudoku.
5. The rule of 45 on one row, column or box, when it leaves three cells or fewer.
6. The rule of 45 over two or three houses, counted against 90 or 135.

The order matters less for its own sake than for what it saves you. Each rung is cheaper to check than the next, and a success low down often makes the higher rungs unnecessary. When cage arithmetic and singles first run dry, the next move is almost always a confined digit: on 125 of the 126 Medium boards that got that far, 236 of 237 Hard and 248 of 252 Expert. The rule of 45 came first on just six boards in all. Many guides tell you to reach for the 45 before anything clever; on our boards, look for a confined digit first.

What does a Hard killer look like from start to finish?

Here is one real Hard board from our generator, seed 25183184, as our solver took it. It needs the rule of 45, including the version over several houses, and it splits into three stages with very different feels:

A move is one step of our solver, which always takes the easiest technique that makes progress. A sweep of cage arithmetic is one pass over every cage. The middle runs from the first move that is not a single or cage arithmetic to the last.

The opening is quick: five one-cell cages and one single. The middle is where the work is. Its first move is a cage digit confined to a row: row 6’s 18-cage can only be 3 + 7 + 8 or 4 + 6 + 8, so the row’s 8 is inside it, the kind of move our combinations guide draws. Then the board sits on nine digits for 27 moves in a row while the rule of 45, confined digits and cage arithmetic chip away at candidates. Thirty moves into the middle comes a move straight from classic sudoku:

Seven moves later the middle is over, and with nine digits on the board the last 72 fall as singles. On this board our solver could have done without confined digits and pairs altogether, though not without the rule of 45.

What does each level of our killer sudoku need?

The levels differ in cage size: one or two cells on Easy, up to three on Medium, four on Hard and five on Expert. Bigger cages have totals that allow more sets, so cage arithmetic settles less on its own. For each board we recorded the hardest rung our solver had to climb:

Each level is 300 boards dealt by our killer generator with fixed seeds, so the first six rows of each column add up to 300. A board beyond our solver still has exactly one answer, but finishing it takes reasoning our solver doesn’t have. The last row counts the digits on the board when the solver made its last move that was not a single or cage arithmetic. Measured October 2026.

So Easy is a cage-arithmetic puzzle and nothing more, and Medium adds confined digits, with the rule of 45 on one board in 25. Hard is where the rule of 45 becomes routine. Expert needs it more often still, and more than one Expert board in ten goes past everything our solver knows. The last row is the encouraging one: the hard part of a killer is the first dozen or so digits. Once the last hard move is made, singles and cage arithmetic do the rest.

When should you reach for the rule of 45?

After the cheaper rungs, but sooner than its reputation suggests. On the Hard and Expert boards that needed it, our solver first used the rule when the board held a median of six digits, about where the easy moves first run out. It isn’t an endgame trick: it is how the middle of a hard killer gets started.

Start with the boxes. A compact cage fits inside a 3×3 box far more often than inside a row, so a box usually leaves few enough loose cells to count. Our rule of 45 guide works through innies, outies and the two-row version on a real Expert board, with the numbers behind that advice.

Stuck in the middle of a hard killer?

Expect a stretch with no new digits. On the boards that needed the rule of 45, the longest run of moves without one was a median of 7 on Medium, 8 on Hard and 9 on Expert. Candidates are still falling during that time, which is progress even when the grid looks the same. When you can’t find a move at all, go up the ladder in order and check each rung properly:

• A digit every set of a cage needs. Check whether that digit’s possible cells in the cage share a row, column or box.
• Plain sudoku. Locked candidates, then pairs. Cage outlines make them easy to miss.
• The rule of 45, boxes first. Then single rows and columns, then pairs of adjacent lines.

If none of that moves the board, you may be on one of the 2% of Hard or 11% of Expert boards that go beyond our solver: each still has exactly one answer, but it takes longer chains of reasoning. Don’t guess. In our game a wrong digit turns red and adds to your mistakes, and Hint fills a cell picked at random rather than the next one you could have reasoned out.

Which habits make killer sudoku easier?

• Pencil marks from Medium up. Every rung above singles works on candidates. In our game, Notes mode holds them, and every correct digit you enter wipes itself from the notes in its row, column, box and cage.
• Say what a cage has left. Once a cage has digits in it, think of the rest as a new cage: a 17 over four cells with a 9 placed is “8 in three cells”, and our chart gives its sets.
• Read sets, not just digits. A cage whose cells allow 3, 4, 6, 7 and 8 can still have only two sets, as the 18-cage on our Hard board did. The digit common to both is the move.
• Keep the chart beside you. The combinations guide has every total for every cage size; nobody needs to learn more than the handful of totals with a single set.
• Practise one level above your comfort. The daily Killer Sudoku climbs from Easy on Monday to Expert on Saturday and Sunday; to check a puzzle copied from paper, our Killer Sudoku solver reports whether its cages have one answer.