Greater-Than Killer Sudoku: Solving Cages With Inequality Signs

Greater-Than Killer Sudoku is a logic puzzle that combines the cage-sum rules of [What Is Killer Sudoku](/blog/what-is-killer-sudoku) with inequality signs between adjacent cells. This variant adds a layer of relational logic, where a '>' or '<' sign dictates which of two neighboring cells holds the larger digit. The signs provide direct, powerful constraints that often solve cells before you even calculate a cage's total sum. This guide will walk you through the core strategies for mastering this engaging hybrid, from interpreting single signs to integrating them with complex cage logic.

By SudokuHint TeamLast updated June 21, 2026

Core Rules: Two Layers of Constraint

In Greater-Than Killer Sudoku, every puzzle contains two distinct types of clues. First, like in standard Killer Sudoku Cage Rules, outlined cages have a small number in the corner indicating the sum of all digits within that cage; digits cannot repeat within a cage. Second, inequality signs ('>' or '<') are placed on the borders between some adjacent cells. These signs are absolute: the digit in the cell facing the open, wider side of a '>' sign must be greater than the digit in the cell facing the pointed side. A '<' sign simply reverses this relationship. These two rule sets interact constantly, with the signs often providing the initial 'foot in the door' to crack a puzzle.

Treat inequality signs as the strongest initial clues. They give you direct numerical relationships between two specific cells.

Key insight: The inequality signs are active constraints on the final grid, just like the 'no repeats in a row' rule. They are not just decorative.

Solving with Inequality Chains

A single sign between two cells is useful, but their real power emerges in chains. When several cells in a row, column, or block are connected by a series of signs, they create a strict order. For example, a sequence A > B > C > D in four cells of a row means the digits must be placed in strictly descending order from A to D. This immediately eliminates many possibilities. You can combine this ordered chain with Sudoku's standard row/column/block constraints. If you know, for instance, that in a row of nine cells, a specific three-cell segment has the order A < B < C, those three cells must contain three distinct digits in ascending order. This can be cross-referenced with other digits already placed in that row to narrow candidates dramatically.

Look for long, unbroken chains of signs along a row or within a 3x3 block. These create a complete mini-puzzle of ordering.
Translate a chain into direct candidate elimination. If Cell A > B and B > C, then candidate '1' can never be in Cell A, and candidate '9' can never be in Cell C.

Integrating Signs with Cage Sums

This is where the puzzle truly shines. The cage sum and the internal inequality signs must both be satisfied simultaneously. You must find combinations of digits that sum to the cage's total AND can be arranged to obey all the '>' and '<' signs within that cage. For example, consider a three-cell cage with a sum of 15 and signs indicating A > B > C. The combination {4,5,6} sums to 15 and fits the order if placed as A=6, B=5, C=4. The combination {7,5,3} also sums to 15 and fits the order as A=7, B=5, C=3. The ordering constraint determines which specific digit goes into which specific cell, not just whether a set of numbers is valid for the sum. This process of finding 'ordered partitions' is a key solving technique. Often, only one ordered set will fit both the sum and interact correctly with digits placed from outside the cage.

Key insight: Always solve for the ordered set within a cage. The sum tells you *what* digits, and the signs tell you *where* they go.

A Common Critical Mistake: Misreading the Sign

The most frequent error in Greater-Than Killer Sudoku is misinterpreting the direction of the inequality sign. This can completely reverse your logic and lead to a dead end. The pointed side of the sign points to the smaller digit; the open side faces the larger digit. Think of the '>' sign as a hungry crocodile—it always wants to eat the bigger number, so its open mouth faces the larger digit. A common misreading is to assume the 'point' indicates the larger number. To avoid this, verbally state the relationship as you look at it: 'The digit on the open side is greater than the digit on the pointy side.' Consistently applying this simple check will save you from countless frustrating errors. For a full breakdown of rules and common pitfalls, see our dedicated guide on Greater-Than Killer Rules.

Strategic Comparison: Greater-Than Killer vs. Standard Killer

How does this variant compare to its parent? The addition of inequality signs fundamentally changes the solving approach. The table below highlights the key differences.

Which Puzzle Should You Play?

Choose Standard Killer Sudoku if you enjoy pure numerical combinatorics and the challenge of dissecting complex sums without extra visual clues. It's a test of your mental arithmetic and set logic. Choose Greater-Than Killer Sudoku if you prefer puzzles that offer immediate, concrete starting points through the inequality signs and enjoy reasoning about relative positions and orders. The signs add a satisfying layer of relational deduction that many solvers find more intuitive to kickstart the solving process. Both are excellent for developing strong logical reasoning, but Greater-Than Killer often feels more accessible at the start due to the direct clues provided by the signs.

Key Facts

▪Greater-Than Killer Sudoku combines the cage-sum rules of Killer Sudoku with inequality signs ('>' or '<') between adjacent cells.
▪An inequality sign is an absolute constraint: the digit on the open side of a '>' sign is greater than the digit on the pointed side.
▪Chains of signs along a row, column, or block create a strict digit order, which is a powerful solving tool.
▪Within a cage, you must find digit combinations that sum to the total AND can be arranged to obey all internal inequality signs.
▪A common mistake is misreading the sign direction; remember the open side faces the larger digit.
▪Unlike standard Killer Sudoku, this variant often provides immediate deductions from the inequality signs before sum calculations.
▪The pointed side of a '>' or '<' sign always indicates the position of the smaller digit in the pair.
▪Solving effectively requires constantly cross-referencing the order from signs with the requirements of cage sums and standard Sudoku rules.

Frequently Asked Questions

What does a '>' sign mean between two cells?

The digit in the cell touching the open, wide side of the '>' must be greater than the digit in the cell touching the pointed side. Think: the open mouth eats the bigger number.

Can digits repeat within a cage in Greater-Than Killer Sudoku?

No. Like standard Killer Sudoku, digits cannot repeat within a single cage, in addition to not repeating in rows, columns, or 3x3 boxes.

How do I start a Greater-Than Killer puzzle?

First, look for long chains of inequality signs, as they establish a clear digit order. Then, look for small cages (2-3 cells) where the sum and signs tightly restrict possible digit pairs or triples.

Is Greater-Than Killer Sudoku harder than regular Killer Sudoku?

Not necessarily. The signs provide extra clues, which can make the start easier. The difficulty depends on the complexity of the cage sums and the sign arrangement.

What is the most common error solvers make?

Misreading the inequality sign direction. Always verify: the open side points to the larger digit, and the pointed side points to the smaller digit.

Do I need to be good at math to solve these?

You need basic addition for cage sums and logical deduction for the signs. The math is simple; the challenge is in the logical integration of all constraints.