Greater Than Sudoku – Easy

Solving Greater Than Sudoku: Rules and Strategies

Greater Than Sudoku is a Sudoku variant. Inequality signs between neighboring cells indicate which side has the larger number.

The variant is also called Inequality Sudoku.

The open side of the sign points to the larger number, the tip to the smaller. Multiple signs can be connected to form a chain of inequalities.

The goal is a completely filled, contradiction-free puzzle. Each move must adhere to the visible clues and already confirmed entries.

Rules

• Each active cell contains exactly one number from 1 to 9.
• Each row contains the numbers 1 to 9 without repetition.
• Each column contains the numbers 1 to 9 without repetition.
• Each standard 3×3 block contains the numbers 1 to 9 exactly once.
• The open side of the sign points to the larger number, the tip to the smaller. Multiple signs can connect to form a chain of inequalities.
• Given numbers are not changed.
• Each final entry must satisfy all rules simultaneously.

Orientation in the Grid

Rows are counted from top to bottom, columns from left to right. For a pair of numbers, the first number indicates the row, and the second the column; (4,7) thus refers to the cell in row 4, column 7.

The examples show a specific intermediate state each time. Blue markings indicate the used prerequisites, red markings an exclusion, and green markings a confirmed result.

Basic Idea for Solving

Transfer individual signs and longer chains into lower and upper bounds first, before entering concrete numbers.

After each secure entry, it's worthwhile to do a quick full review of the affected units and additional clues. This creates a chain of small, understandable steps.

1. Complete an Almost Full Row

In unit Row 1, everything except cell (1,2) is filled. Numbers 1, 2, 3, 4, 5, 6, 8, 9 are visible; only 7 is missing from the valid options.

Therefore, 7 goes into (1,2). The move requires no guess: the other values of the considered unit are fully visible in the image.

2. Complete an Almost Full Column

In column 1, everything except cell (2,1) is filled. Numbers 2, 3, 4, 5, 6, 7, 8, 9 are visible; only 1 is missing from the valid options.

Therefore, 1 goes into (2,1). The move requires no guess: the other values of the considered unit are fully visible in the image.

3. Fully Read the Relevant Region

In the 3×3 block 1, everything except cell (1,2) is filled. Numbers 1, 2, 3, 4, 5, 6, 8, 9 are visible; only 7 is missing from the valid options.

Therefore, 7 goes into (1,2). The move requires no guess: the other values of the considered unit are fully visible in the image.

4. Read a Single Inequality Sign

The sign between (1,1) and (1,2) requires that the target value is less than 9.

The candidate 9 violates this order and is eliminated. The solution value 7 is on the correct side of the inequality.

5. Convert a Chain of Inequalities into Value Ranges

The signs form the chain (1,1) > (1,2) > (1,3). Three different, strictly decreasing values are needed for this.

The upper end cannot be 1 or 2, and the lower end cannot be 8 or 9. Such range limits are then intersected with candidates in rows, columns, and blocks.

6. Combine Chain and Sudoku Candidates

At the shown intermediate state, the boundary values of the chain (1,1) > (1,2) > (1,3) are already known.

Only the number 7 fits between 9 and 5 among the still valid Sudoku candidates. It is placed in (1,2).

7. Combine Multiple Units in a Single Cell

In (1,2), several units are still incomplete. After elimination by all associated rows, columns, and regions, only 7 remains.

The candidate set for (1,2) is therefore {7}. Such single-cell candidates often only emerge after checking all types of units simultaneously.

Typical Solving Process

1. Immediately fill complete rows, columns, and relevant regions.
2. Note only candidates that all normal units allow for open cells.
3. Then apply the additional rule of this puzzle type to these candidates.
4. Enter only values with clear reasoning.
5. After each entry, recheck all affected units and hints.
6. Repeat the review until the grid is complete.

Common Mistakes

• Holding the tip for the larger side: The open side points to the larger number.
• Focusing only on individual signs: Chains provide stronger value ranges.
• Guess too early: Multiple remaining candidates are not yet a reason to guess.
• Not rechecking after an entry: A single value can change multiple units and hints at once.

Tips for Beginners

• Start with units or hints that have especially much visible information.
• Write down small candidate sets instead of mingling possibilities mentally.
• Always check a candidate against each rule affecting its cell.
• Count secure exclusions as real progress, even if no value is set yet.
• If no move is visible, purposefully switch from rows to columns, regions, and additional hints.

Greater Than Sudoku becomes clear once normal units and additional hints are consistently reevaluated after each secure step. Small, fully justified inferences lead more reliably to the goal than early guessing.