Greater Than Sudoku Rules: How to Play and Solve Inequality Clues

Greater than sudoku is a standard 9×9 sudoku with one extra rule: some neighboring cells have > or < signs between them. Those signs tell you which side must contain the larger digit. The usual sudoku rules still apply, so every row, column, and 3×3 box must contain the digits 1 through 9 exactly once.

If you already know regular sudoku, this variant is easy to learn because the structure does not change. What changes is the kind of information you can use at the start. Instead of relying only on givens, you can also use inequality clues to shrink candidate lists, force high and low digits, and create cleaner logical deductions.

What Is Greater Than Sudoku?

Greater than sudoku, sometimes called inequality sudoku or greater than less than sudoku, adds comparison signs between adjacent cells. If one cell must be larger than the cell next to it, the puzzle shows that relationship directly. These clues can appear horizontally, vertically, or both depending on the puzzle design.

The important point is that this is still sudoku, not a different number puzzle. You are still building a valid 9×9 grid with nine 3×3 boxes. The inequality signs are extra constraints layered on top of the normal rules.

Greater Than Sudoku Rules

1. Use the standard sudoku rules

Each row must contain the digits 1 to 9 exactly once. Each column must contain the digits 1 to 9 exactly once. Each 3×3 box must also contain the digits 1 to 9 exactly once.

2. Follow every inequality sign

If a > sign appears between two adjacent cells, the value on the wider side of the symbol must be greater than the value on the pointed side. If a < sign appears, the smaller value is on the pointed side and the larger value is on the open side.

Some puzzle publishers draw the signs directly between cells. Others use small arrows or wedge-shaped markers. The idea is the same: one side must be smaller, and the other side must be larger.

3. Only adjacent cells are affected

An inequality clue tells you about the two cells it touches. It does not automatically apply to the whole row or column. You still need normal sudoku logic to connect that local clue to the rest of the grid.

4. No sign means no extra comparison clue

If there is no symbol between two neighboring cells, there is no additional greater-than or less-than rule there. Standard sudoku rules are the only restriction in that spot.

How to Solve Greater Than Sudoku Step by Step

Start with the extremes: 1 and 9

The fastest opening move in greater than sudoku is to think about extremes. A cell that must be greater than one neighbor and greater than another is unlikely to be small. A cell that must be smaller than multiple neighbors is unlikely to be large.

In particular, 1 can never sit on the larger side of an inequality, and 9 can never sit on the smaller side. That sounds obvious, but it creates immediate eliminations across the grid.

Use short inequality chains

If cell A is greater than cell B, and cell B is greater than cell C, then A must also be greater than C. You do not know the exact digits yet, but you do know their order. These short chains help you rule out impossible candidate sets very quickly.

For example, three cells in a row that descend left to right cannot be 2, 1, 3 because the third value would need to be smaller than 1. Chains are especially useful when they pass through a row or column that already has several digits placed.

Combine inequality clues with row, column, and box restrictions

This is where most real progress happens. Suppose a cell must be larger than its left neighbor, but the row already contains 7, 8, and 9. That cell can no longer be one of the largest digits. If its box also removes 5 and 6, the inequality may reduce it to a single candidate.

Greater than sudoku becomes much easier when you stop treating the signs as a separate layer. Read every clue together with ordinary sudoku scanning.

Look for forced middle values

Many players focus only on 1 and 9, but middle digits matter too. If one cell must be greater than two nearby cells and smaller than another, its candidate range narrows fast. A cell trapped between smaller and larger neighbors often becomes a short list even before many givens are placed.

Check vertical clues carefully

Horizontal signs are easy to see, but vertical comparisons are where many solving mistakes happen. If a symbol sits between an upper and lower cell, make sure you read it from the correct orientation before eliminating candidates. Misreading one vertical clue can break the whole puzzle.

Quick Example

Imagine two adjacent cells in the same row with a > sign between them, so the left cell must be larger than the right cell. If the left cell’s candidates are {2,4,6} and the right cell’s candidates are {4,5}, the clue changes both lists immediately.

The left cell cannot be 2 or 4 because it must be greater than the right cell. The right cell cannot be 5 because the left cell would need to be larger than 5 but does not have a candidate above 5 except 6. After applying the clue properly, the pair becomes left {6} and right {4,5}, and then the right cell becomes {4,5} subject to the rest of the row, column, and box. In many real puzzles, one more standard elimination would finish the pair.

Common Greater Than Sudoku Mistakes

Reading the symbol backward

This is the most common beginner mistake. Always pause for a second and identify which side is larger before writing candidates.

Ignoring standard sudoku structure

Some solvers focus so hard on the signs that they forget to scan rows, columns, and boxes. The best deductions usually come from combining both rule sets, not from using only one.

Assuming every sign gives an immediate solve

An inequality clue often narrows possibilities without solving the cell outright. That is still useful progress. Do not force a number just because one side looks larger.

Confusing greater than sudoku with futoshiki

Futoshiki is a related inequality puzzle, but it usually does not use sudoku’s 3×3 boxes. Greater than sudoku keeps the full sudoku structure and adds comparison clues on top.

Tips to Solve Greater Than Sudoku Faster

Mark high and low pressure cells first

Cells connected to several inequalities are often the best starting points. They carry more information than isolated cells.

Revisit chains after every placement

One solved cell can tighten an entire run of inequalities. After each confirmed digit, scan nearby signs again before moving to another part of the grid.

Use notes, but keep them small

Full notation can help on harder greater than sudoku puzzles, but short candidate lists are usually enough. If a clue already tells you a cell must be relatively high or low, do not clutter the square with every remaining digit.

FAQ

Is greater than sudoku the same as inequality sudoku?

Yes. Many publishers use those names interchangeably. Some also describe it as greater than less than sudoku.

Is greater than sudoku the same as futoshiki?

No. They are similar because both use inequality clues, but greater than sudoku still includes the standard 3×3 sudoku boxes. Futoshiki usually works as a Latin-square puzzle without sudoku boxes.

Can a greater than sudoku puzzle have no given digits?

Yes. Some puzzles rely almost entirely on the inequality clues. In those cases, the comparisons provide enough structure to produce a unique solution.

What should I look for first in greater than sudoku?

Start with the most constrained areas: cells connected to several inequality signs, cells near fixed digits, and places where 1 or 9 are impossible because of the clue direction.

Conclusion

The greater than sudoku rules are simple: solve a normal sudoku grid, then obey every > and < clue between neighboring cells. The challenge comes from combining those comparisons with regular row, column, and box logic. Once you start looking for extremes, chains, and relative high-low relationships, the puzzle becomes far easier to read.

If you enjoy this kind of variant, explore more rule-based twists and compare how different clue types change the way a sudoku grid opens up.