Play Futoshiki — Free

What is Futoshiki?

Futoshiki is a Japanese logic puzzle whose name means "not equal" — a neat clue to how it works. You are given a small square grid, five cells wide and five cells tall on the vygam version, and your goal is to fill it so that every row and every column contains the numbers 1 to 5 exactly once. That part alone makes it a Latin square, the same "no repeats in any line" idea that sits at the heart of Sudoku. What makes Futoshiki its own puzzle is a scattering of greater-than and less-than signs printed between some pairs of neighbouring cells. Every number you write has to keep those inequalities true, so the signs quietly rule out possibilities and turn the whole board into a chain of deductions.

Because it blends the tidy structure of a Latin square with the ordering logic of inequalities, Futoshiki feels both familiar and fresh. There is no arithmetic to do — the digits are just five symbols with a natural order, and the only "maths" is knowing that 4 is bigger than 2. A handful of cells arrive already filled as givens to get you started, and from there you reason your way to the single correct answer, one forced number at a time. Every puzzle on vygam is hand-crafted with exactly one solution, so you can always reach the finish by pure logic — never by guessing. It is a quick, satisfying brain workout that fits neatly into a coffee break, and the small grid means you can solve a whole puzzle in the time a Sudoku is barely getting started.

How to Play Futoshiki

The rules that decide whether the grid is finished are simple, and a placement is wrong whenever it breaks one of them:

• a number from 1 to 5 appears more than once in the same row;
• a number from 1 to 5 appears more than once in the same column;
• two filled cells joined by a sign do not respect the inequality — for example a smaller number sits on the larger side of a >.

Reading the signs is the whole trick, and it matches the maths symbols you already know. The open, wide end of the sign always faces the bigger value; the narrow point aims at the smaller one. A sign that reads left-cell > right-cell demands a larger number on the left, while left-cell < right-cell demands a larger number on the right. The vertical signs between stacked cells work the same way — the wide side simply points up or down. Lean on the given numbers first: they anchor their row and column, and any sign attached to a given instantly narrows what its neighbour can be.

Futoshiki Tips & Strategy

Futoshiki looks tiny, but a good order of attack makes even the Hard boards fall into place. These techniques turn the signs from decoration into your most powerful solving tool.

1. Follow the chains of inequalities

   When several signs line up in a row — say a < b < c < d — the values are forced into strict order. On a 1-to-5 grid, a chain of three signs that all point the same way squeezes the possibilities hard: the smallest cell in a length-four increasing chain can only be 1 or 2, and the largest can only be 4 or 5. Trace every run of signs before you write anything, because a single long chain often pins down two or three cells at once.

2. Find the forced 1s and 5s at chain ends

   The numbers 1 and 5 are the anchors of any inequality, because 1 can never be on the large side of a sign and 5 can never be on the small side. A cell that sits at the "less-than" end of a chain and has a sign pointing away from it is a prime candidate for 1; a cell at the "greater-than" end is a prime candidate for 5. Hunt these extremes out first — each one you place removes a value from its whole row and column and usually triggers a cascade of further deductions.

3. Cross-hatch like Sudoku

   Even without the signs, Futoshiki is a Latin square, so the scanning habits from Sudoku pay off. Pick a value, say 3, and check which rows and columns already contain it; the cell where its last row and last column intersect, with nowhere else legal to go, must be a 3. Combine this with pencil notes: jot every candidate in a cell, then erase them as neighbouring numbers and signs rule them out. A cell left with a single note is a guaranteed answer.

4. Let the signs break your ties

   Often the Latin-square logic alone leaves a cell with two candidates and no way to choose — this is exactly where the inequalities earn their keep. Look at the sign touching that cell and the value on the other side. If the cell must be greater than a neighbour that is already 4, it can only be 5; if it must be less than a neighbour that is 2, it can only be 1. Always check a stuck cell's signs before you move on, because the answer is usually hiding one comparison away.

Difficulty Levels & Puzzles

vygam ships three tiers of hand-crafted Futoshiki, and each puzzle is authored with a single guaranteed solution reachable by logic alone. Easy boards give you plenty of starting numbers and short, friendly sign chains — perfect for learning how the inequalities behave and for a relaxed, quick win. They are the ideal place to practise reading a > and a < at a glance and to get comfortable with the "1 to 5, once each" rhythm of a row.

Medium puzzles pull back some of the givens so you rely more on cross-hatching and on the signs to break ties, while Hard puzzles hand you the fewest clues and the longest chains, so a run of inequalities often carries more weight than the numbers on the board. Your fastest completion is stored separately for each difficulty in your browser, so you can chase a personal-best time on Easy while slowly working up to the Hard set. Tap New puzzle at any time to move on to the next board in the current tier — the collection cycles so there is always another grid waiting.

Futoshiki vs Sudoku & Other Logic Puzzles

If you already enjoy Sudoku, Kakuro, Nonogram or Minesweeper, Futoshiki will feel like a close cousin with a twist of its own. Like Sudoku it is built on the Latin-square rule — fill each line with a set of symbols and never repeat one — but it swaps Sudoku's 3×3 boxes for inequality signs, and shrinks the grid to a brisk 5×5. That makes an individual Futoshiki much faster to finish, while the signs add a layer of ordering logic that Sudoku never asks for. Where a Sudoku solver counts what is missing from a box, a Futoshiki solver compares neighbours and follows chains of "bigger than" and "smaller than" across the board.

Compared with Kakuro, which hides its constraints inside crossword-style sums, Futoshiki keeps everything visible: the signs sit right on the board, so there is no adding to do and the puzzle is friendlier to newcomers. Against a picture-forming puzzle like Nonogram or the deduction-under-uncertainty of Minesweeper, Futoshiki is purer — there is always a next logical step and never a moment where you must gamble. That combination of a small, quick grid and completely transparent rules is exactly why Futoshiki has become a favourite warm-up for puzzle fans, and why it plays so well as a short, thinking break in your browser.

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