Killer Sudoku combinations chart: 2 and 3 square cages

By David, 26 October 2026

In Killer Sudoku the grid is split into cages, each with a total in the corner. The numbers in a cage add up to that total, and no number appears twice in the same cage. Most cages on a typical board have two or three squares, so knowing what those can hold does a lot of the work for you.

This page lists every combination for two and three square cages. It was worked out by computer, checking every possible set of numbers, so nothing is missing. For how to play and the rule of 45, see our Killer Sudoku page.

How to read the charts

Each row is one cage total. The middle column shows every set of numbers that adds up to it with no repeats. The last column says how many sets there are.

The fewer the options, the more useful the cage. A cage with one option tells you exactly which numbers it holds. A cage with two options often lets you rule numbers out of the rest of its row, column or box.

The order inside a cage is not shown, because the chart cannot know it. A two square cage of 3 is 1 and 2, but you still need the rest of the board to tell which square gets the 1.

Two square cages

A few things stand out:

• 3, 4, 16 and 17 have only one answer. These are the cages to look for first on any board.
• 10 is the least helpful. It has four options, and the only number it rules out is 5.
• Even totals never use half the total. A cage of 8 cannot be 4 and 4, because numbers cannot repeat in a cage. That is why 4 is missing from that row.
• The chart is symmetric. A cage of 5 has the same number of options as a cage of 15, because each answer can be flipped: swap every number for 10 minus that number.

Three square cages

The pattern is the same as for two squares. The two smallest totals, 6 and 7, and the two largest, 23 and 24, have only one answer. The middle totals, 14 to 16, have eight options each and tell you very little on their own. The number of options climbs towards the middle and falls away again.

Using the charts while you play

1. Find the single option cages first. Write their numbers in as notes. A cage of 23 across three squares means each square gets the notes 6, 8 and 9.
2. Look at what a cage cannot hold. A three square cage of 8 is either 1, 2 and 5 or 1, 3 and 4. Both include a 1, so that cage holds the 1 for its row if it sits in a single row. No other square in that row can be a 1.
3. Combine with the rule of 45. When the rule of 45 gives you the total for a single square or a pair of squares, these charts tell you straight away what they can be.
4. Cross off as you go. Once one number in a cage is placed, the chart for the remaining squares gets much shorter. A three square cage of 15 with a 9 already placed leaves a two square total of 6, which is 1 and 5 or 2 and 4.

Bigger cages

Four and five square cages follow the same rule. Only the two smallest and two largest totals have a single answer:

Everything in between has several options, so for big cages it usually pays to place a few numbers around them first.

Try it

Open Killer Sudoku in another tab and keep this chart beside it. Easy uses mostly two and three square cages and gives you a few starting numbers. Medium has the same small cages with no starting numbers at all. Every puzzle is checked to have exactly one answer, so there is always a move to find without guessing.

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