The fastest way to get better at Futoshiki is to let the signs do the work early: start with the 1s and the top number, read signs as chains, and after every number you place, look along its row and column. We measured these tips on all 150 of the game’s levels, and the numbers below come from those tests.
These build on how to solve Futoshiki. If you haven’t played before, start with the rules.
Solving tips
1. Start with the 1s and the top number
The larger side of a sign can’t be 1, and the smaller side can’t be the top number. Go along each row and column looking for the one square left that could take a 1, or the top number. On every one of the game’s levels, the first move comes from the signs, and on 135 of the 150 it places a 1 or the top number.
2. Read signs as chains
A single sign rules out just one number on each side. Two or three signs pointing the same way do far more: in a row of four, a chain of three settles every square. On the game’s levels, more than half the moves that come from the signs need a chain of two or more of them: 65% on Easy, 63% on Medium and 51% on Hard.
3. Do the signs first, then count
The signs matter most early on. Of the numbers placed from the signs, 86% come in the first half of an Easy solve, 82% on Medium and 79% on Hard. After that, most of the work is counting what each row and column still needs.
4. Look at the lines you just changed
Every number you place sits in a row and a column that now need one fewer. On the game’s levels, the next number goes in one of those two lines 64% of the time on Easy, 63% on Medium and 61% on Hard. Check them before searching the rest of the grid.
5. Write notes from 6×6 up
Every Easy level finishes without notes. On Medium, 15 of the 50 levels need a pair and 10 a hidden pair, and those are hard to see without notes. On Hard, the sign work alone comes up about 5 times per level: rounds where the signs rule numbers out without placing any. Notes are where you keep what they tell you.
6. Try what-if on a square with two numbers left
When nothing else works on a Hard level, what-if is the way through, and it’s quickest on a square with only two numbers left: rule one out and the square is settled. About half the what-if steps on the game’s Hard levels (49%) are on a square like that.
Tips for playing on PeerPuzzles
7. Use the keyboard
On a computer, type a number to place it, and the arrow keys move between squares. N turns notes on and off, Backspace clears a square, and U or Ctrl/Cmd + Z undoes a move. The number pad shows how many of each number are still to place.
8. Let the red marks and Stuck? help
A repeated number turns red the moment you place it, and so does a sign that doesn’t hold. And if you’re stuck, Stuck? (or H) highlights where to look and names the technique, without filling anything in for you. If one of your numbers is wrong, it rings that square first.