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Killer Sudoku Tips and Strategies: What to Scan First

Most advice about killer sudoku is about arithmetic — memorise the cage combinations, learn the rule of 45, practise your sums. All of it helps. But when beginners stall on a grid, the arithmetic is rarely the problem. They know what to look for. They just look in the wrong order.

Here's the order that works.

Scan order matters more than arithmetic

A killer sudoku grid gives you a fixed amount of information, and every deduction you find reduces the remaining possibilities. The question is never "what do I know" — it's "which move collapses the most candidates for the least effort".

Two habits follow from that. Start where the candidates are fewest, which usually means the smallest cages. And resolve the forced stuff before you start speculating, because every deduction you bank early makes the later decisions cheaper.

Beginners do the opposite. They open with the interesting-looking five-cell cage in the middle, get stuck, then fill notes into every empty cell and lose track of what they were doing.

The four-pass scan

Run these four passes in order. On an easy grid the first two can give you a strong start; on a hard grid you'll cycle back through all four repeatedly, which is normal.

Pass 1 — The smallest cages

A two-cell cage has at most a handful of possible digit pairs. A five-cell cage can have more possible sets and many more arrangements of those digits. So sweep the board for every cage of two or three cells and resolve what you can before touching anything larger.

The sets worth knowing by sight are the ones with a single possibility: 3 and 17 in two cells, 6 and 24 in three, 10 and 30 in four. Cross-check each set against digits already placed in the rows, columns and boxes of the cage. A digit cannot go in a cell where it would create a repeat, which can narrow the available arrangements.

Pass 2 — Extreme totals

Very low and very high cage totals narrow themselves, because there simply aren't many ways to reach them. A cage totalling 7 in two cells is 1+6 or 2+5 or 3+4 — three options. A digit already placed in a shared row, column or box can rule out an option, but it does not automatically eliminate two.

Work both ends toward the middle. The cages near 10 and 11 (in two cells) and near 15–16 (in three) are the ambiguous ones, and they're the last thing you should spend time on.

Pass 3 — The rule of 45 checkpoints

Every row, column and 3×3 box holds 1–9 exactly once, so every one of them sums to 45. That gives you a way to work backwards from a total.

Find a box where cages contained entirely inside it cover all but one or two cells. Subtract those cage totals from 45; what remains is what the uncovered cells must add to. If a cage crosses the box boundary, do not subtract its entire total unless you also account for its cells outside the box.

A box whose cages total 39, with a single cell outside all of them, means that cell is 45 − 39 = 6. That's a digit placed, and it cost you one subtraction.

This is the move that separates comfortable solvers from stuck ones. If you only take one thing from this page, take this: when you're stuck, stop looking at cells and start looking at boxes.

Pass 4 — Row and column cross-checks

Only now look at individual rows and columns. If eight cells in a row contain eight different digits, the last cell takes the missing digit. A cage that straddles a box boundary tells you something about the cells on each side of it — that shared constraint is often the only way forward in a hard grid.

This pass is useful when the earlier scans no longer produce a forced move. You are evaluating several constraints at once, so it helps to bank the easy deductions first. Still cross-check rows and columns whenever you place a digit; the passes are a scanning order, not a reason to ignore a constraint.

Notes: use them late, not early

Pencilling candidates into every cell feels productive and usually isn't. Full notation turns a clean grid into a wall of digits, and the small ones are harder to scan than the big ones.

Consider it a tool for a specific situation: you've run the four passes, you're genuinely stuck, and you need to see all the candidates for one or two cells at once to spot the contradiction.

Fill notes for the cells you're actively working on, not the whole board. Then clear them when you move on.

Check and Hint are two different lessons

Both buttons can help you move forward, but they do different things. Check highlights conflicting or incorrect entries without changing them. Hint fills one correct cell.

Check tells you something is wrong, or narrows down where. That's information you can still learn from — you go back, find the deduction you got wrong, and understand why.

Hint places a digit for you. It ends the stall without explaining it, and the underlying mistake stays in your head.

If you're playing to improve rather than to finish, use Check first and only reach for Hint when you've genuinely run out of ideas.

Five habits that slow beginners down

1. Opening with the biggest cage. It can have many possible arrangements, so it is often a slower starting point. Look for forced small cages and extreme totals first.
2. Writing the combination into the cell. Knowing a cage is 1+2+4 tells you which three digits are in it, not which digit is where. That second question is what the row and column rules are for.
3. Ignoring box boundaries. Cages that cross into another box are the richest source of deductions in the grid, and the easiest to overlook.
4. Guessing. It works often enough to feel viable, and it destroys your ability to tell a real deduction from a lucky one.
5. Restarting when stuck. Ninety seconds of re-running pass 3 beats starting over. The grid hasn't changed; your scan has.

FAQ

How do I get faster at killer sudoku?

Get faster at the scan order, not at the arithmetic. Run the four passes in sequence, every time, until it's automatic. Most of the speed comes from knowing where to look next, not from adding faster.

Should I start with the hardest cages or the easiest?

Easiest, always — meaning the smallest ones, and the ones with the most extreme totals. They have fewer possibilities, so they resolve with less work. The ambiguous mid-range cages are the last thing you should touch.

What's the fastest way to solve a killer sudoku grid?

Small cages first, then extreme totals, then check every box against 45, then work the rows and columns. When you stall, go back to the boxes rather than the cells. And use the keyboard — digits 1–9, arrow keys to move, N for notes — it's noticeably quicker than tapping cells.

If you want the underlying rules first — what cages are, the full combinations table, and a worked example of the 45 rule — start with the killer sudoku rules. Then come back and play today's killer sudoku.