Greater Than Sudoku: Rules and Solving Strategy

Read every inequality as a directional rule

Greater Than Sudoku uses the familiar 9x9 grid where every row, column, and 3x3 box contains 1 through 9 exactly once. Between selected neighboring cells, a greater-than or less-than sign shows their numerical order. The open side faces the larger value and the point faces the smaller one. If A is greater than B, A cannot be 1 and B cannot be 9. More importantly, their candidate lists must support each other. If A can only be 4, 5, or 6 while B can only be 2, 3, or 4, many pairings disappear because the value in A must remain strictly larger. If later A falls to 4 and B also falls to 4, the relationship becomes impossible, revealing an error or an invalid candidate assumption. Some puzzles place inequalities between many cells, while others use them sparingly. Shapedoku does not assign numerical size to its glowing shapes, so inequalities are not part of its classic boards, but the candidate discipline used on Hard and Extreme Shapedoku carries over directly.

Turn long chains into useful bounds

A single inequality gives a small amount of information. A chain gives much more. Consider four cells with A less than B less than C less than D. Since the digits must be distinct, A cannot be 7, 8, or 9 because three larger digits still need to follow. B cannot be 1 or 9, while D cannot be 1, 2, or 3. Longer chains tighten the ranges further. If a chain of five cells is strictly increasing, the first cell can be at most 5 and the last must be at least 5, with stronger limits often coming from their crossing units. Do not assume the chain uses consecutive digits. A sequence such as 1, 3, 6, 9 is valid. The correct method is to keep enough smaller or larger candidates available at each position. When one cell narrows, propagate the new bound through the whole chain instead of updating only the immediate neighbor.

Use candidate support instead of simple minimums and maximums

Bounds are a fast first pass, but exact candidate support is stronger. Suppose A must be less than B. If A has candidates 2, 5, and 7 while B has 4 and 6, candidate 7 in A has no larger partner and can be removed. Candidate 5 survives because B could be 6, while candidate 2 survives with either 4 or 6. Now look the other way: if B contains 4 and 6, the 4 needs a smaller candidate in A, which 2 provides. This two-way check prevents weak candidates from lingering. Inequalities that meet in one cell are especially useful. A cell that must be greater than two neighbors but less than a third may be forced into a narrow middle range. Combine that with row, column, and box restrictions and exact placements often appear. Once an inequality elimination creates a single or subset, return to classic Sudoku logic before extending the chain farther. The extra signs are most useful when they simplify the ordinary grid.

1. Translate every sign into a clear smaller-cell and larger-cell relationship.
2. Use chain length to set rough lower and upper bounds before listing exact candidates.
3. Remove any candidate that has no compatible value on the other side of an inequality.
4. Propagate new bounds through entire inequality chains after every placement.
5. Combine intersecting inequalities with row, column, and box restrictions.
6. Rescan for classic singles and subsets whenever candidate ranges shrink.