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Futoshiki for Beginners: Start Here

New to Futoshiki? Learn the two rules on a 5×5, then get used to reading the signs: the point faces the smaller number, a sign rules numbers out on both sides, and signs pointing the same way make a chain. With those and some counting, you can finish every Easy level in the game. This page puts the guides in that order, with a six-row warm-up to check yourself before you move up a size.

Open Futoshiki full screen for more sizes, saved progress and best times.

Your path, in order

  1. Learn the rules. The Futoshiki rules page solves the game’s first level step by step. The one idea to take away: each number once in every row and column, and every sign holds.
  2. Solve your first 5×5 from the signs. Look for a square less than a 2 (it’s 1), and for the one square in a line that could take the 1 or the 5.
  3. Count every line. When a square’s row and column leave it only one number, or a number has only one place left in a line, fill it in.
  4. Learn the techniques one at a time. How to solve Futoshiki covers all six; the first three are all you need on Easy.
  5. Do the warm-up below. Six rows, each practising an idea from the guides above.
  6. Pick up speed. The Futoshiki tips page adds where to look after every move.
  7. When a puzzle goes wrong, read the six common mistakes. The big one is putting a number in before it’s certain.
  8. Move up a size when you’re ready (see below).

Warm-up: six rows

Each is a single row, so it needs each number once: 1 to 4 in a row of four, 1 to 5 in a row of five. Work out what you can be sure of, then open the answer. Every answer is everything that row can tell you on its own.

1. Less than 2

Warm-up 1: Less than 2 A row of four. The third square is a 2, and the square before it is less than 2. What can you be sure of? 2
Show the answer
Warm-up 1, answered A row of four. The third square is a 2, and the square before it is less than 2. Certain: square 2 is 1. 1 2

Square 2 is 1: it’s less than 2, and 1 is the only number that is. Squares 1 and 4 are 3 and 4, but either way round works.

2. A full chain

Warm-up 2: A full chain A row of four with three less-than signs, all pointing the same way. What can you be sure of?
Show the answer
Warm-up 2, answered A row of four with three less-than signs, all pointing the same way. Certain: square 1 is 1, square 2 is 2, square 3 is 3, square 4 is 4. 1 2 3 4

1, 2, 3, 4. Each square is bigger than the one before, and there are only four numbers to go round.

3. Smaller than both neighbours

Warm-up 3: Smaller than both neighbours A row of four ending in a 4. The second square is less than the squares on both sides of it. What can you be sure of? 4
Show the answer
Warm-up 3, answered A row of four ending in a 4. The second square is less than the squares on both sides of it. Certain: square 2 is 1. 1 4

Square 2 is 1. The first three squares share 1, 2 and 3, since the 4 is taken, and square 2 is smaller than both the others, so it gets the smallest. Squares 1 and 3 are 2 and 3, either way round.

4. A clue at the top of a chain

Warm-up 4: A clue at the top of a chain A row of four. The first square is less than the second, which is less than a 3 in the third square. What can you be sure of? 3
Show the answer
Warm-up 4, answered A row of four. The first square is less than the second, which is less than a 3 in the third square. Certain: square 1 is 1, square 2 is 2, square 4 is 4. 1 2 3 4

1, 2, 3, 4. Two numbers less than 3, in order: 1 then 2. That leaves 4 for the last square.

5. One clue, two signs

Warm-up 5: One clue, two signs A row of four. The first square is less than a 2 in the second; the third is less than the fourth. What can you be sure of? 2
Show the answer
Warm-up 5, answered A row of four. The first square is less than a 2 in the second; the third is less than the fourth. Certain: square 1 is 1, square 3 is 3, square 4 is 4. 1 2 3 4

1, 2, 3, 4. Square 1 is less than 2, so it’s 1. That leaves 3 and 4 for the last two squares, and the sign puts the 3 first.

6. Where does the 1 go?

Warm-up 6: Where does the 1 go? A row of five. The second square is less than the squares on both sides of it, the fourth is a 3, and the fifth is more than 3. What can you be sure of? 3
Show the answer
Warm-up 6, answered A row of five. The second square is less than the squares on both sides of it, the fourth is a 3, and the fifth is more than 3. Certain: square 2 is 1. 1 3

Square 2 is 1. Ask where the 1 can go: not square 1 or square 3, which are both bigger than square 2; not square 4, which is the 3; and not square 5, which is more than 3. That leaves square 2. The other squares can still go more than one way.

When to move up a size

You’re ready for Medium (6×6) when you can finish Easy levels without guessing, you read signs down columns as easily as across rows, and you look for the 1s and the top number without thinking about it.

The bigger sizes don’t just take longer; they ask for more. Every Easy level finishes with the signs and counting. On Medium, 20 of the 50 levels also need a pair or a hidden pair, so it’s time to start writing notes. On Hard (7×7), every level needs what-if, about 11 times each.

Next steps

Questions

Is Futoshiki good for beginners?

Yes. The two rules take a minute to learn, and every Easy level in the game finishes with the signs and two simple ideas: a square with one number left, and a number with one place left.

Do I need to be good at maths?

No. There’s no adding up, only knowing which of two numbers is bigger, from 1 to 5 on a 5×5.

How long should a puzzle take?

As long as it takes. PeerPuzzles keeps your best time for every level, so you can see yourself improve without trying to.