Hard Greater Than Sudoku

Inequality signs between cells show which is larger. No given digits — all placements are deduced from the signs alone.

Easy Medium Hard Expert

Hard Greater Than Sudoku. Long inequality chains, cross-chain box interactions, and few or no given digits — full candidate tracking is essential.

4
7
3
9
8
4
5
1
2
5
8
3
1
6
3
9
3
4
5
2
3
9
7
6
4
8
3
∨ ∨ ∧ ∨ ‹ › › ‹ ∨ ∧ ∧ ‹ ‹ ∨ ∨
Mistakes
0/3
Score
-
Time
00:00
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Progress0%

What is Greater Than / Less Than Sudoku?

Difficulty
★★★☆☆
3/5
Constraint Type
Cell Relationships
Typical Givens
18–24
Avg. Solve (Hard)
32 min

Solving Techniques for Hard Level

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

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Techniques to Master at Hard

  • Hidden Pairs technique — Bound propagation removes middle candidates invisibly; recount each box after walking the chains, because hard greater-than grids hide pairs behind out-of-date ranges.
  • X-Wing technique — Extreme digits have the fewest chain-legal positions — 1 can never sit above a > sign, 9 never below — so X-Wings on 1 and 9 are the natural hard-mode tools.

Average Solve Time by Difficulty

Easy
7 min
Medium
16 min
Hard
32 min
Expert
58 min
Want a full walkthrough of rules, strategies, and solving steps? How to Play Greater Than / Less Than Sudoku →

Related Variants

Kropki Sudoku

Refines your adjacent-cell reasoning with exact relationships — difference of 1 and ratio of 2 instead of plain order.

XV Sudoku

Adjacent pairs constrained by sums rather than order, with a negative constraint on every unmarked edge.

Odd / Even Sudoku

Another value-property variant: parity shading halves candidates the way your inequality chains bound them.

Frequently Asked Questions — Hard Greater Than Sudoku

What makes hard Greater Than Sudoku difficult?
Hard puzzles have fewer or no given digits — the inequalities alone must drive the solve. Long inequality chains, complex box interactions, and the need to simultaneously track value ranges and standard candidacy across the entire board make hard Greater Than very demanding.
How do I handle long inequality chains at hard difficulty?
Enumerate the minimum chain: if you have a chain of length N, the smallest possible values are 1, 2, 3 … N for the chain in ascending order, and the largest possible values are (10-N), …, 8, 9 in descending order. Cross-referencing with rows and columns quickly eliminates most candidates.
Should I use pencil marks for hard Greater Than Sudoku?
Yes. Hard puzzles require tracking both the standard candidates (which digits are still possible in each cell) and the range bounds derived from inequalities. Write the minimum and maximum possible digit next to each cell's candidates to keep the bounds visible.
What is the hardest type of deduction in hard Greater Than Sudoku?
The most difficult deductions involve cross-chain interactions: a constraint from one inequality chain eliminates a value from a cell that then tightens the range of a different chain in the same box. These cascades are hard to see without a complete candidate grid.
How long does a hard Greater Than Sudoku take?
Expect 35–60 minutes. If you're stuck, look for the longest inequality chain on the board and fully enumerate its valid digit sequences — this usually provides the breakthrough.

More questions? See the full Greater Than Sudoku guide.