Hard Greater Than Sudoku
1
4
5
6
9
6
1
8
3
7
8
6
9
4
2
9
9
5
3
7
4
6
8
8
2
8
9
How to play Greater Than Sudoku
Standard Sudoku rules apply. Extra rule: the inequality sign between two adjacent cells (› ‹ ∧ ∨) always points from the larger cell to the smaller cell. If A › B, then A > B.
About Greater Than / Less Than Sudoku
Difficulty
★★★☆☆
3/5
Constraint Type
Cell Relationships
Typical Givens
18–24
Avg. Solve (Medium)
16 min
Greater Than Sudoku (also called Futoshiki-style Sudoku) places < and > inequality signs between adjacent cells. The sign indicates which of the two cells must hold the larger value. Some variants replace all given digits with inequality signs; others provide a hybrid. The constraints create chains of reasoning: if A > B > C > D, then A ≥ 4, B ≥ 3, C ≥ 2, D ≥ 1.
Solving Techniques
| Technique | Description | Level |
|---|---|---|
| Chain Inequality — Minimums | Link inequalities in a chain: if A > B > C, then A ≥ 3, B ≥ 2, C ≥ 1. Use these minimums to prune candidates immediately. | Beginner |
| Chain Inequality — Maximums | In the chain A > B > C > D, also bound from above: A ≤ 9, B ≤ 8, C ≤ 7, D ≤ 6. | Beginner |
| Inequality Propagation | After placing a digit, check all inequality arrows from that cell and eliminate impossible values from its neighbours. | Intermediate |
| Forced Single via Range | When an inequality chain reduces a cell's valid range to a single digit, place it directly. | Intermediate |
Average Solve Time by Difficulty
Easy
7 min
Medium
16 min
Hard
32 min
Expert
58 min