Killer Sudoku
Play

Strategy

Killer Sudoku Strategy & Tips

A practical guide to solving Killer Sudoku: memorise the forced cage combinations, use the 45 rule and innies and outies, keep pencil notes, and let the row, column, and box do the rest.

Play Killer Sudoku

The core idea

Every cage is a small equation

A cage is a set of digits that add to a known total, with no repeats. That means each cage has a short list of possible digit sets, and nearly every technique in Killer Sudoku is about shrinking those lists: with the sudoku constraints (row, column, box), with the 45 total of every region, and with the other cages around it.

The techniques below go from the ones you need on Easy to the ones that unlock Expert. Try them on the board — pencil notes and the hint button are there to help you learn.

Techniques

Six techniques, in the order to learn them

  1. Technique 1

    Learn the forced cage combinations

    Some totals have exactly one solution: two cells adding to 3, 4, 16, or 17; three cells adding to 6, 7, 23, or 24; four cells adding to 10 or 30. Recognising these on sight is the single biggest speed-up. Even without knowing the order of the digits, you know the cage’s set, which lets you strike those digits from the notes of every cell that shares a row, column, or box with the whole cage.

  2. Technique 2

    Use the 45 rule

    Every row, column, and box holds 1 through 9, so it adds to 45. If cages lie entirely inside a region except for one cell whose cage reaches outside it, add the totals of the fully-inside cages and subtract from 45: the difference is that one cell, called an innie. Mirror that with cages that cover a region but overflow it by a single cell — add their totals, subtract 45, and the difference is the cell outside the region, an outie. Innies and outies often give an outright digit.

  3. Technique 3

    Note candidates, then eliminate

    For a cage of n cells with total s, the allowed digits are the union of all n-digit sets that add to s. Pencil those in, then remove any digit that already appears in the same row, column, or box, or that is already placed elsewhere in the cage. When a digit can appear in only one cell of a row, column, or box, it goes there.

  4. Technique 4

    Look for cage overlap in rows and boxes

    If two cells in one row form a cage that must be {8, 9}, then no other cell in that row can be 8 or 9. The same logic works for triples such as {1, 2, 3}. Cages that lie entirely within one row, column, or box are strong sources of eliminations.

  5. Technique 5

    Work from the extremes

    High and low totals constrain a cage the most: a cage of three cells summing to 23 has just {6, 8, 9}, while one summing to 15 has eight possible sets. Start with the tightest cages, place what you can, and let each digit shrink the options for the next cage.

  6. Technique 6

    Use hints to learn, not to skip

    A hint reveals one digit without costing a mistake. Because the puzzle is solvable by logic, you can look at the revealed digit and work out which technique would have found it. Use it on Hard and Expert to study a stuck position rather than to finish the grid.

Worked example

An innie in action

Take a row. Suppose most of it is covered by cages that lie completely inside the row, and exactly one cell of the row belongs to a cage that reaches into the next row. The row adds up to 45, so add the totals of the fully-inside cages and subtract from 45 — what is left is the value of that one cell. That cell is an innie, and you have an outright digit.

Now the mirror image. If the cages that touch a row all lie inside it except one that hangs out by a single cell, add up every cage total that touches the row and subtract 45. The result is the value of the cell outside the row — an outie. The same arithmetic works for columns and 3×3 boxes, and it is the workhorse of Hard and Expert puzzles.

Pitfalls

Mistakes that cost lives

  • Repeating a digit inside a cage

    The most common error: a cage of 10 over three cells is not 3+3+4. Digits never repeat inside a cage, so always check that your combination uses distinct digits.

  • Guessing instead of eliminating

    With a three-mistake limit, a 50/50 guess is expensive. When two digits remain, look for another cage or region that separates them before committing.

  • Forgetting the row, column, and box

    A cage total can be satisfied and still put two 7s in one row. Always check the sudoku constraints alongside the cage arithmetic.

  • Skipping notes on harder levels

    On Hard and Expert the cage combinations overlap in ways that are impossible to hold in your head. Keep notes on and let auto-clearing prune them as you place digits.

Next

Ready to practise?

Start on Easy to build your instincts for two- and three-cell cages, then move up one level at a time. For the rules and the cheat sheet of forced totals, read how to play Killer Sudoku.