Greater Than Sudoku – Medium

Greater Than Sudoku

Greater Than Sudoku is a variant of Sudoku with inequality signs between neighboring cells. The normal Sudoku rules still apply, but additionally, the signs between the cells must be satisfied.

Each sign indicates which of the two neighboring cells contains the larger value. This creates many local size relationships that significantly restrict candidates.

Basic Rules

• Each row contains the numbers 1 to 9 exactly once.
• Each column contains the numbers 1 to 9 exactly once.
• Each 3x3 block contains the numbers 1 to 9 exactly once.
• An inequality sign between two cells must be satisfied.
• The open side of the sign points to the larger number.
• A cell that must be larger than a neighbor cannot be 1.
• A cell that must be smaller than a neighbor cannot be 9.

Strategies for Solving

1. Order two missing numbers using an inequality

Inequalities are especially powerful when only two numbers are missing in a region.

In the following example, the two open spots in row 1 are missing only 5 and 7. Additionally, between the two open cells, it holds that row 1, column 2 is greater than row 1, column 3.

The missing numbers are 5 and 7. Since column 2 must be larger than column 3, column 2 cannot be 5. Therefore, row 1, column 2 is 7, and row 1, column 3 is 5.

2. Evaluate chains of inequalities

If multiple cells are connected by inequalities in sequence, a order is established. A chain like A > B > C means: A is larger than B and B is larger than C. This means C cannot be high and A cannot be low.

3. Recognize extreme values

A cell that must be larger than multiple neighbors is a good candidate for a high number. A cell that must be smaller than several neighbors is a good candidate for a low number. This observation alone does not always set a number but significantly narrows candidates.

Typical solving process

1. First check normal Sudoku steps.
2. Then look for areas with two or three open cells and matching inequalities.
3. Use inequalities to order missing numbers correctly.
4. Eliminate 1 from cells that must be larger than a neighbor.
5. Eliminate 9 from cells that must be smaller than a neighbor.
6. Check chains of inequalities, as they restrict multiple candidates simultaneously.

Common mistakes

• Rushing to guess instead of using the additional rule as a reliable exclusion.
• Only checking rows and columns and overlooking the special marking of the puzzle.
• Entering a number that fits locally but violates the special rule.
• Not updating candidates after each new entry.
• Reading a marking incorrectly or applying it to the wrong cells.

Tips for Beginners

• Start like with a normal Sudoku with well-filled rows, columns, and regions.
• Then specifically check the special rule. Often, early safe exclusions are made here.
• Always ask yourself: Which numbers are actually allowed and which are excluded by a rule?
• Enter a number only if it can be uniquely derived.
• If you get stuck, change your perspective: from rows to columns, from regions to the special rule, or from individual cells to candidates.

Greater Than Sudoku combines Sudoku logic with size comparisons. The signs do not provide direct numbers but organize candidates, making many otherwise open situations clear.