How to play

Futoshiki rules and how to play

This is the solving guide. The Futoshiki library is for picking a grid. Here you learn the four rules that finish one.

What is Futoshiki?

Futoshiki is a Latin square with inequalities between some neighbouring cells. DIGIGMA boards are 4×4, 5×5, or 6×6. Some digits are already given. Those cells never change. There is one solution.

Goal of the game

Fill every empty cell with a number from 1 to N so each row and each column uses every number once, and every printed inequality is true.

Rules

Rule 1

Fill the grid with numbers 1 to N. On a 4×4 board that is 1–4. On a 6×6 board that is 1–6.

Rule 2

Each number appears once in every row.

Rule 3

Each number appears once in every column.

Rule 4

Respect every inequality. The point of the sign faces the smaller number.

Every puzzle can be solved logically. You do not need to guess.

How to read the signs

The sign sits between two cells, never inside a cell. Horizontal signs look like < and >. Vertical signs look like ∧ and ∨. In every case the point of the sign faces the smaller cell.

2 is smaller than 4
2<4

2 < 4. The point of < faces 2, the smaller number.

A vertical inequality
2∧5

∧ points up, so the top cell is smaller: 2 is less than 5. A ∨ would point down to the smaller cell.

When you’re stuck

  • Find a cell squeezed by a tight inequality (a 1 next to <, or an N next to >).
  • Scan a row or column that already has most of its numbers.
  • Clean Draft marks that a new placement has made impossible.
  • Do not guess. A DIGIGMA grid always has a forced next step.

On Practice, Hint shows a next idea. Reveal fills the grid. Neither is available on Ranked.

Common mistakes

  • Reading a sign backwards: the point always faces the smaller number.
  • Repeating a digit in a row or a column.
  • Treating a vertical ∧ / ∨ as decoration instead of a comparison.
  • Guessing instead of using the tightest inequality.

Practical tips

  • Start with the smallest and largest possible numbers forced by a sign.
  • Draft a cell that still has two or three candidates, then look at its row.
  • Open a grid from available Futoshiki boards once the four rules feel automatic.

FAQ

Which way does the inequality point?
The point of the sign faces the smaller number, whether the sign is horizontal (< >) or vertical (∧ ∨).
Do I need to guess?
No. Every DIGIGMA Futoshiki has one solution and a path of forced placements.
What sizes are there?
4×4, 5×5, and 6×6. The keypad only shows 1 through N for that board.
What is Draft?
Candidate marks you write in a cell until only one number remains. They are a memory aid, not a score.
What should I do when I get stuck?
Re-read the tightest signs, clean Draft, and scan almost-complete rows and columns. Guessing is not the method.

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