Inequality Grid: use a comparison chain before choosing exact values
A strict chain can place bounds on its cells even when it does not solve them. Combine those bounds with Latin-row exclusions instead of treating the signs as decoration.
Worked examples use the Standard board unless a different size is stated. Hard and Expert may change the board dimensions or amount of information to track.
Read the geometry without importing Sudoku rules
Inequality Grid is a Latin-square puzzle. Each row and each column contains every number from 1 to the board width exactly once. It has no Sudoku-style boxes. A missing comparison sign between adjacent squares leaves no extra ordering rule there, although both squares still belong to their ordinary row and column constraints.
For a horizontal sign, the pointed end faces the smaller number. The vertical symbols follow the same convention: an upward-pointing sign places the smaller value above the larger one, while a downward-pointing sign places it below. Read the relation aloud if its orientation is unclear before entering a number.
Use the length of a strict chain
Imagine four adjacent squares in a Standard-size row related as A less than B, B less than C, and C less than D. The allowed values are 1 through 4, and every step must strictly increase. The only possible sequence is therefore 1, 2, 3, 4. A chain spanning the complete range determines the values without inspecting another row.
A shorter chain provides bounds instead of a complete answer. On a five-wide board, A less than B less than C implies that A is at most 3 and C is at least 3. It does not force A to be 1 or C to be 5. There may be spare values outside the chain, and row or column information must decide whether those values belong inside it.
Combine a sign with missing row values
Consider a separate four-wide row reading 2, blank, blank, 1, with the first blank less than the second. Its missing values are 3 and 4. The sign orders them, so the blanks must be 3 then 4. Without that comparison, the row alone would permit either order.
Now check the crossing columns. If an assumed row position would duplicate an existing column value, the problem is not solved by ignoring that column. Review earlier editable entries or the deduction that produced the assumed position. A comparison is one constraint among several, and every constraint must remain true together.
Keep an entry separate from a tentative bound
This implementation offers a number keypad and Clear, rather than a pencil-mark layer for candidate ranges. If a chain only establishes that a square is at least 3, entering 3 would assert more than you have proved. Keep the bound mentally or on separate paper until another constraint selects an exact value.
Immediate conflicts are highlighted when filled values repeat or violate a comparison. Their absence does not prove that a tentative number will extend to a solution. Undo returns to the previous entry; Restart removes your entries while retaining the original clues. Use the chain’s ordering to explain a value before committing to it, then recheck the row, column and every comparison touching that square.
An original guide for this site's implementation. Found an unclear step? Let us know.