If you've ever finished a Sudoku and thought "that was good, but I wish there was more to it," Futoshiki might be exactly what you're looking for. It takes the satisfying logic of filling a grid with unique numbers and adds inequality constraints that force you to think in a completely different way.

I'd never heard of it until recently, and now I'm a bit hooked. Here's what I've learned about where it comes from and why it's worth your time.

What Does Futoshiki Actually Mean?

The name comes from the Japanese word futoshiki (not equal sign), which translates to "inequality"[^1]. That single word captures the entire concept of the puzzle: you're placing numbers in a grid while respecting inequality signs between certain cells.

You might also see it called "More or Less" or "Unequal" in English-language puzzle books, but Futoshiki is the name that stuck internationally.

A Brief History

Futoshiki was developed by Tamaki Seto in 2001[^1]. It emerged during the golden age of Japanese logic puzzles, riding the wave that Sudoku had started. Where Sudoku had proved there was a massive global appetite for number-based logic puzzles, Futoshiki offered a twist: instead of 3x3 boxes, you got inequality constraints.

The puzzle made its way to the UK when The Guardian newspaper started publishing it on 30 September 2006, with an article headlined "If you were seduced by sudoku, prepare for futoshiki fever"[^1]. It's since been picked up by The Daily Telegraph, The Times, and the Dundee Courier, among others[^1].

It never quite reached the mainstream fame of Sudoku, which is a shame. The smaller grid sizes (typically 4x4 to 6x6 compared to Sudoku's 9x9) make individual puzzles quicker to solve, and the inequality constraints add a layer of deductive reasoning that Sudoku doesn't have.

How It Works

The rules are straightforward:

Fill every cell with a number from 1 to N (where N is the grid size)
Each number appears exactly once in every row
Each number appears exactly once in every column
Respect the inequality signs between adjacent cells

A solved Futoshiki puzzle is what mathematicians call a Latin square -- a grid where each symbol appears exactly once in each row and column[^1]. The inequality constraints are what make it a puzzle rather than just a maths exercise: they narrow down the possibilities and give you a logical path to the solution.

The solving technique is a mix of elimination (like Sudoku) and chaining inequalities. For example, if you see A < B < C in a 4x4 grid, you immediately know A can only be 1 or 2, and C can only be 3 or 4. That kind of cascading deduction is what makes Futoshiki feel different from other grid puzzles.

What Does the Research Say About Logic Puzzles and Your Brain?

I want to be honest here: there isn't specific peer-reviewed research on Futoshiki and cognitive health. It's too niche for that. But there's a solid body of research on logic puzzles more broadly, and it paints an interesting (if nuanced) picture.

The Positive Findings

A 2019 study found that people who regularly engage in word and number puzzles perform on cognitive tests as if they were eight to ten years younger than their actual age[^2]. The researchers observed a dose-response relationship -- the more frequently people did puzzles, the better they performed on attention, reasoning, and memory tasks.

A 2018 study published in Frontiers in Aging Neuroscience found that puzzle-solving engages eight distinct cognitive domains: visual perception, constructional praxis, mental rotation, processing speed, cognitive flexibility, working memory, reasoning, and episodic memory[^3]. The researchers also found that sustained puzzle engagement over a lifetime showed protective associations with cognition.

And a 2022 study from Duke University found that crossword puzzles outperformed computerised brain training games in slowing memory loss, with puzzle solvers showing 0.5% to 1% less brain shrinkage in the hippocampus over 18 months[^4].

The Important Caveats

Marcel Danesi, a professor at the University of Toronto and author of research on puzzles and cognition, notes that "much of the research in this domain turns out to be ambiguous"¹. The correlation-vs-causation problem looms large: do puzzles make your brain sharper, or do people with sharper brains gravitate toward puzzles?

What brain scientists do seem to agree on is that novelty matters. Trying a new type of puzzle -- one your brain hasn't already optimised for -- is likely more beneficial than grinding through your 10,000th easy Sudoku². This is actually a solid argument for picking up Futoshiki if you're already comfortable with Sudoku: same general territory, but your brain has to work in a different way.

Why Futoshiki Specifically?

Beyond the general puzzle-and-brain research, there are a few things that make Futoshiki particularly appealing:

It's quick. A 4x4 puzzle takes a couple of minutes. A 6x6 might take ten. You can fit it into a coffee break without committing to a 45-minute Sudoku marathon.

It scales well. The jump from 4x4 to 5x5 to 6x6 is a genuine difficulty curve, not just "more of the same." Each size introduces meaningfully more complexity because the inequality chains get longer and interact in more ways.

It exercises different mental muscles than Sudoku. Sudoku is primarily about elimination within boxes, rows, and columns. Futoshiki adds relational reasoning -- you're constantly thinking about relative values, not just absolute ones. That "A < B < C" chaining is a different cognitive skill than scanning a row for missing numbers.

It's accessible. You don't need to be a maths person. The numbers are just symbols -- you're doing logic, not arithmetic.

Give It a Go

We've just added Futoshiki to Games I Play with three difficulty levels: Easy (4x4), Medium (5x5), and Hard (6x6). It supports pencil marks for noting candidate numbers, undo for when you inevitably paint yourself into a corner, and keyboard controls for desktop players.

Play Futoshiki now and see if it clicks for you. If you're anything like me, a "quick 4x4 before bed" will turn into three 6x6s and a mild obsession with inequality chains.

References

Puzzles and the Brain - Marcel Danesi, Psychology Today, 2009
Can Sudoku and Crosswords Improve Your Brain Health? - Right as Rain by UW Medicine