Guides

How to solve Killer Sudoku: a step-by-step method

A Killer Sudoku solve is not a race to calculate every cage. It is a sequence of constraints: first use cages with very few digit sets, then let rows, columns and boxes decide placements, and use the rule of 45 only where a complete unit creates a useful difference. This walkthrough is a reusable method rather than a solution to one disposable grid. Return to the first step whenever a puzzle feels crowded.

Read the smallest and tightest cages first

Mark single-cell cages immediately. Then inspect two-cell and three-cell cages with extreme totals: 3 or 17 in two cells, 6 or 24 in three cells. These have one digit set, or very few. Record the set, not an order. A two-cell 3 is {1,2}; a two-cell 17 is {8,9}. Check whether either digit is already blocked by the row, column or box of one cage cell. That can place a digit without any further arithmetic.

Reduce each promising cage with its three units

Every cage cell belongs to a row, column and box. After recording a cage set, compare each digit with those units. If one cage cell cannot take 1 because its column already has 1, the set remains valid but 1 must be placed in another cell of that cage. If a whole set contains a digit that has no legal location in the cage, remove the set. Place only a digit with a complete proof, then update the three affected units and return to nearby cages.

Let one solved cage create the next one

A solved cage changes the board exactly like a given Sudoku digit. Revisit cages that share its row, column or box before moving across the grid. Often a new placement removes the final alternative in a nearby cage, exposes a classic Naked or Hidden Single, or narrows a pair. This local follow-up is more efficient than recalculating every sum. Killer Sudoku alternates naturally between cage logic and normal Sudoku logic.

Use the rule of 45 when a unit is almost accounted for

Every complete row, column and box contains 1 through 9 and therefore totals 45. Add the cages wholly inside a unit and compare with 45; the difference is the sum of the cells or cage parts crossing its boundary. For two complete units use 90, for three use 135. Choose a region with only a few crossing cells. The rule of 45 is powerful when it leaves a small, testable remainder—not when it creates another long list of possibilities.

Finish with a verification loop, never a guess

Before a difficult placement, state the proof: cage set, no-repeat rule, row, column, box, or a 45-difference. After placing it, check the cage total and scan the three affected units. If the board stalls, do not force the next number; leave broad middle-sum cages marked and seek a more restrictive cage or a classic Sudoku pattern. This loop keeps the solve explainable and makes errors easy to locate early.

Use the method on a real Killer board

Start an easy Killer puzzle and apply the order once from top to bottom. When a cage proof needs more detail, open the related lesson or jump into a targeted practice position.

Killer Sudoku Play Easy Learning path

Cage combinations Rule of 45 Innies and outies

Frequently asked questions

What should I look at first in a Killer Sudoku?

Start with single-cell cages, then small cages with extreme totals. They have the fewest possible digit sets and often interact immediately with their rows, columns or boxes.

When should I use the rule of 45?

Use it when a row, column, box or small group of complete units is almost covered by known cage totals and only a few cells cross the boundary. It is most useful when the remaining sum is small and specific.

Can I solve Killer Sudoku with only cage arithmetic?

No. Cage sums restrict digit sets, but normal Sudoku rules place digits and remove options. Strong solves alternate between cage logic and row, column and box exclusions.

How do I avoid guessing in Killer Sudoku?

Write only sets supported by the cage sum and no-repeat rule, then place a digit only when a unit or a sum proof forces it. If a cage still has several valid sets, leave it and work on a more restrictive constraint.