Inequality (Futoshiki) vs Sudoku

Inequality — called Futoshiki in Japan — is the closest relative to Sudoku in the number-puzzle family. Both puzzles use the same Latin-square base: fill an N×N grid so every row and column contains each digit from 1 to N exactly once. The difference is the type of information you get. Sudoku gives you specific digits as starting clues. Futoshiki gives you < and > signs between adjacent cells — relational constraints instead of fixed values. That one change reshapes the entry point, the solving technique, and the difficulty curve.

WHAT THEY SHARE

Both puzzles are Latin squares: an N×N grid where every row and column contains each digit from 1 to N exactly once. The solving vocabulary overlaps almost completely. Naked singles, hidden singles, and candidate elimination all work identically in both puzzles. If you're an experienced Sudoku solver, your core toolkit carries over directly.

Both puzzles are solved by pure deduction — no guessing required at any difficulty tier. If you find yourself guessing in either puzzle, you've missed a forced move.

THE ONE KEY DIFFERENCE

Sudoku provides direct information: specific digits pre-filled in specific cells. Each given cell tells you exactly what one cell contains.

Futoshiki provides relational information: signs between cells telling you which is larger. A sign tells you something about two cells simultaneously, but doesn't tell you the value of either one directly.

This is both less and more. It's less because no cell is immediately placed. It's more because each sign constrains two cells at once — and chains of signs constrain entire rows.

SIDE BY SIDE

Grid structure
Sudoku: 9×9 with nine 3×3 boxes
Futoshiki: N×N, typically 5×5 or 7×7 (no box constraint)

Starting information
Sudoku: given digits in specific cells (17–35 of 81)
Futoshiki: inequality signs between adjacent cells + optional givens

Constraint type
Sudoku: uniqueness in row, column, and 3×3 box
Futoshiki: uniqueness in row and column + relational ordering

Box constraint
Sudoku: yes — three overlapping constraints per cell
Futoshiki: no — only row and column

First move
Sudoku: scan for cells where only one digit fits (naked single)
Futoshiki: find extremal cells — greater than all neighbours must hold N

Arithmetic required
Sudoku: none
Futoshiki: light — count arrows per cell for min/max bounds

THE INEQUALITY FIRST MOVE

In Sudoku, the first forced placement comes from scanning rows, columns, and boxes for cells where only one digit remains as a candidate. The given digits constrain the candidates directly.

In Futoshiki, the first move comes from the inequality signs. Count how many < and > arrows each cell has. A cell greater than all its neighbours must hold the maximum value (N). A cell smaller than all its neighbours must hold 1. These are immediate placements — the Futoshiki equivalent of a Sudoku naked single.

The chain technique amplifies this: if cells A < B < C in the same row of a 5×5 grid, then A ∈ {1, 2, 3}, B ∈ {2, 3, 4}, C ∈ {3, 4, 5} — three cells narrowed simultaneously from one chain of two signs.

WHAT DOESN'T TRANSFER

Sudoku's 3×3 box constraint is the single biggest differentiator. Pointing pairs, box-line reduction, and X-wings all depend on the box. Futoshiki has no equivalent. Futoshiki is purely a row-column puzzle.

The given-digit scan doesn't apply in Futoshiki grids that start without any pre-filled digits at all (some Futoshiki puzzles use signs exclusively). In that case, the inequality chains are your only entry point — there's nothing analogous in Sudoku.

Chain-tracing is uniquely Futoshiki. Following a chain of inequality signs across a row to derive bounds is a skill with no Sudoku analogue. The first few Futoshiki grids will feel unfamiliar even to an expert Sudoku solver until the chain instinct develops.

WHICH IS HARDER?

At equivalent difficulty tiers, Futoshiki is typically harder for Sudoku players in the short term. The chain-tracing technique takes time to internalize, and the absence of the 3×3 box constraint means Sudoku's most powerful tool is unavailable.

Once chain-tracing clicks, Futoshiki's deduction speed can actually exceed Sudoku's for some grid configurations — a full inequality chain across a row places the entire row in one pass, which Sudoku rarely achieves at the same difficulty level.

Experienced Futoshiki solvers often describe it as "Sudoku with a different opening move." That's accurate — once past the initial chain scan, the rest of the solve is standard Latin-square elimination.

WHEN TO MAKE THE SWITCH

If you play Sudoku: try Futoshiki when you want to apply your row/column deduction skills with a different information source. Your candidate-elimination techniques work identically — the new skill is reading the inequality chains before starting them.

If you play Futoshiki: try Sudoku when you want the third constraint layer (the 3×3 box) that opens up different elimination patterns. Sudoku's box constraint is what makes techniques like pointing pairs and X-wings possible — tools that Futoshiki never produces.

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