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Futoshiki

Each number once in every row and column, and every sign between two squares has to hold.

Type
Logic
Takes
about 3-10 min
Result in
seconds

Futoshiki

~3-10 min

  1. Fill each row and column with 1 to the grid's size, each number once.
  2. Every sign must hold: 2 < 4 across, and down the point is on the smaller side.
  3. Tap a square, then a number.

Keyboard: arrows, the digits, Backspace.

Your result: —

How it's measured

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What are the rules of Futoshiki?

Futoshiki is a square grid you fill with the numbers from 1 up to its size: 1 to 5 on a 5 × 5. Each number appears once in every row and once in every column. Between some neighbouring squares there is a sign, and it must hold: the open side of < or > faces the larger number. A few numbers may be given to start you off.

Choose a 4 × 4, 5 × 5, 6 × 6 or 7 × 7 grid (5 × 5 is picked to begin with). Tap a square, then a number on the pad; on a keyboard, the arrow keys move and the digits fill. Signs between rows are drawn as ∧ and ∨, with the point on the smaller number. Two equal numbers in a line, or a sign that doesn't hold, are outlined as soon as you make them.

How do you solve Futoshiki?

  • Start at the ends of the scale. A square that is less than another can never hold the largest number, and a square that is greater can never hold 1.
  • Follow chains of signs. On a 5 × 5, four squares each less than the next need four different numbers in order, so the first is 1 or 2 and the last is 4 or 5.
  • Find singles. A square with one number left takes it, and so does a number with one place left in its row or column.
  • Use pairs. Two squares in a line that can only be 2 or 3 hold the 2 and the 3 between them, so every other square of that line can cross both out.

How is your Futoshiki time calculated?

Your result is the time from Start until every square is filled and every rule holds. Beside it are the times you used Check, which marks any wrong number, and Hint, which fixes a wrong number if there is one and otherwise fills an empty square. There is no rating: no published typical time exists for puzzles built like these, so the page doesn't invent one.

Does every Futoshiki here have exactly one answer?

Yes. Each puzzle is made in your browser when you press Start. It begins as a full grid with every sign shown; numbers and then signs are taken away one at a time, each only if a solver using the moves above can still finish without guessing. The finished puzzle's answers are then counted by a separate search, and it is shown only if there is exactly one. The site's tests make puzzles of every size and check both again.

What does Futoshiki mean?

Futoshiki is Japanese for “inequality”, which is what the signs are. Without them it would be a Latin square, a grid where each number appears once per row and column. Sudoku adds boxes to that rule, Calcudoku adds sums and products in cages, and Skyscrapers adds clues around the edge about which towers you can see.

Questions

Which way does the sign point?
The open side faces the larger number, so 2 < 4 and 4 > 2. Between rows, ∧ means the top number is smaller and ∨ means it is larger: the point is always on the smaller side.
Do I ever have to guess?
No. Every puzzle is checked before you see it: a solver using only the moves people use finishes it, and a separate search finds exactly one answer.
What does a hint do?
It corrects a wrong number if you have one; otherwise it fills one empty square with its answer. The number of hints is shown with your time.
Can I use the keyboard?
Yes. The arrow keys move between squares, the digits fill one, and Backspace clears it.
What is a good time?
There is no published average for puzzles of this size and design, so the page doesn't give one. Compare your own times on one grid size.