Solving easy killer sudoku

Easy killer sudoku is the tier where cage-sum patterns do the work that classic givens used to. Most easy killer puzzles ship with a handful of givens — five or six, sometimes none — and the cages plus their sums carry the rest. The new mental shift, the one that turns easy classic into easy killer, is learning to read a cage as a constraint rather than as a visual grouping. A 2-cell cage summing to 3 isn't decoration; it tells you those two cells contain a 1 and a 2 in some order, and that information eliminates a 1 and a 2 from every other cell in the cage's row, column, and box. If you've never played killer before, our piece on meeting killer sudoku covers the rules.

The cage-sum patterns to know

A handful of cage sums have only one possible digit set. Memorising them is the cheapest improvement most easy killer solvers can make.

Two-cell cages: 3 = 2, 4 = 3, 16 = 9, 17 = 9. Each of these has exactly one valid digit pair (since duplicates aren't allowed inside a single cage). Spotting one instantly eliminates those two digits from every other cell in the cage's row, column, and box.

Three-cell cages: 6 = 3 and 24 = 9 are the two with single-set solutions. 7 = 4 and 23 = 9 have one common pattern but technically allow others; in easy killer they almost always resolve to the standard pattern.

These cage-sum patterns are called killer pairs (and triples). They appear in nearly every easy killer puzzle, often as the first move on a fresh grid. Walking the cages once before placing any digit, marking the killer-pair cages, frequently knocks two or three eliminations into place before the solve has really started.

The 45-rule, lightly

The 45-rule — the foundational killer technique — appears at easy in its simplest form. The digits 1 through 9 sum to 45, so every row, column, and box must sum to 45. If a row contains four cages totalling 38, the fifth cage in the row must total 7. That's already enough to narrow the cage's possible digits dramatically.

At easy, the 45-rule fires on rows and columns that have most of their cages contained within them. Box-level 45 calculations and complex innie/outie applications start at medium and hard. At this tier, the technique is simple arithmetic: add the cages, subtract from 45, see what's left.

Singles and scanning, the same as classic

Once the cage patterns and the 45-rule have done their initial work, easy killer reduces to the same scanning pattern as easy classic. Naked singles and hidden singles carry most placements. The scanning rhythm — placement, scan the row/column/box you just changed, find the next single — is identical to easy classic, just applied to a grid that started with cages instead of givens.

The piece on the two moves that solve most easy puzzles covers naked and hidden singles in detail; everything in that article applies at easy killer too. The only difference is that the initial constraint set comes from cage sums rather than scattered givens.

When easy killer stalls

Easy killer stalls in two characteristic ways.

Cage-sum tunnel vision. Spending too long on the arithmetic ("what digits sum to 14") at the expense of the cage's grid position. Easy killer puzzles are joint constraints — cage sum AND row/column/box position — and when one fails to break a stall, switching to the other usually does. If a cage's possible digit sets don't narrow on the sum alone, look at where its cells sit and what's already in the surrounding regions.

Ignoring the cage geometry. Two cages that share a row, column, or box can't both contain the same digit in those shared cells. The constraint is just standard sudoku elimination applied through cage outlines, but it's easier to forget when the cages are visually separated. Walking the cage shapes once before each new region check is a habit worth building from easy on.

Two habits to drop

Treating cages as decoration. Cages aren't visual grouping; they're constraints that fire constantly through the solve. When a cage's cells are all placed, its outline can be mentally turned off. When a cage is partially resolved, the remaining cells' digit options collapse fast. Reading the cage state actively — not just at the start of the puzzle but throughout — saves real time.

Skipping the cage-pattern memorisation. The two-cell and three-cell killer pairs above each take a few seconds to recognise once memorised. Solvers who don't memorise them spend longer on every puzzle, doing the arithmetic from scratch each time. Five minutes of memorisation pays back across hundreds of puzzles.

When the cage patterns start firing on first inspection and the 45-rule applications feel automatic, you're ready for medium killer, where the 45-rule starts firing on multiple axes and killer pairs apply to a wider range of cage sums. Easy killer is the tier worth lingering at while the cage-as-constraint instinct becomes natural — that mental shift is most of what killer's harder tiers will ask for.