THE SHORT VERSION
Inequality (Futoshiki): an N×N Latin-square grid. Some pairs of adjacent cells have a < or > sign between them. Every sign must be true in the final grid — the cell on the smaller side of < holds a smaller digit than the cell on the larger side. No 3×3 box constraint — rows and columns only.
Skyscraper: an N×N Latin-square grid. Numbers around the border tell you how many "buildings" (cells) of increasing height (digit) are visible when you look inward along that row or column from that edge. A taller building blocks every shorter one behind it. Often played on a 9×9 grid with the 3×3 box constraint included.
Both reduce to Sudoku if you remove their extra clue type. That is where the similarities end.
SIDE BY SIDE
Base constraint
Inequality: 1–N once per row and column (no box rule)
Skyscraper: 1–N once per row, column, and 3×3 box (9×9)
Extra clue type
Inequality: < / > signs between adjacent cells (inside the grid)
Skyscraper: view-count numbers on the grid border (outside the grid)
What one clue constrains
Inequality: two specific cells (direct pair comparison)
Skyscraper: an entire row or column (global visibility)
Clue density
Inequality: many signs scattered throughout the grid
Skyscraper: 4×N clues around the border (at most one per row end)
Primary technique
Inequality: chain propagation (A < B < C forces A to be small, C to be large)
Skyscraper: permutation enumeration + Latin-square scanning
WHAT STAYS THE SAME
The Latin-square constraint is the backbone of both puzzles. Every Sudoku technique — naked singles, hidden singles, pointing pairs — applies to the inner grid in both variants. When you are stuck on the extra clues, falling back to pure Sudoku scanning often unlocks a cell, which then feeds back into the variant logic.
Both puzzles are solved by propagating constraints, not by guessing. In Inequality, placing a digit tightens the inequality chains that pass through that cell. In Skyscraper, placing a digit eliminates row permutations that are inconsistent with the edge clues. In both cases, a single correct placement cascades through the grid.
HOW THE REASONING DIFFERS
Inequality reasoning is local and chained. A single < or > sign constrains exactly two cells. But those cells sit inside rows and columns, and the row/column constraint connects them to every other cell in those lines. The solving pattern is: identify forced extremes (a cell that must hold the max or min digit in its line because of the inequality chains through it), then use those extremes to eliminate candidates elsewhere.
Skyscraper reasoning is global and enumerative. A border clue constrains an entire row or column at once. You enumerate all valid orderings of the digits that produce the given view count from that direction, then find which digit positions are the same across all valid orderings — those are forced. This is more like working with a set of possible permutations than with a chain of pairwise constraints.
In practice, Inequality solvers tend to scan for forced-extreme cells first; Skyscraper solvers tend to work from the border inward. Both strategies then converge on the same Sudoku scanning loop, but they enter it from different directions.
WHICH IS HARDER?
At comparable grid sizes, Skyscraper is generally harder. The permutation enumeration required for border clues is more cognitively demanding than chain propagation, and the standard Skyscraper grid (9×9 with box constraint) is larger than the typical Inequality grid (4×4 to 6×6). A medium Inequality and a medium Skyscraper at the same stated tier typically require a different amount of mental effort.
Hard Inequality can become very demanding when the inequality signs are sparse — you're left doing most of the work from the Latin-square base with only a handful of comparison constraints to help. Hard Skyscraper requires holding the permutation sets for multiple rows simultaneously while applying box constraints. Both flavours of hard are genuinely difficult; they just stretch different mental muscles.
WHEN TO MAKE THE SWITCH
If you play Inequality: try Skyscraper when the chain-propagation technique feels automatic. Your Latin-square foundation transfers directly. The new challenge is learning to read visibility clues as constraints on whole-row permutations rather than on individual pairs.
If you play Skyscraper: try Inequality when you want a puzzle where the constraints live inside the grid rather than around the border. The chain-propagation style is a useful complement to Skyscraper's border-inward reasoning — it trains faster candidate-elimination for adjacent cells.
Playing both builds two complementary sides of constraint-logic reasoning: local pairwise chains (Inequality) and global permutation analysis (Skyscraper). Solvers who know both tend to see constraint propagation paths that single-variant players miss.