Suguru

How to solve Suguru (Tectonic): five moves, no guessing

Updated Tuesday, October 27

To solve a Suguru, start with the regions that leave no choice, then cross out every digit that touches a digit already written: each square soon has a single candidate left. Every Gridarium suguru can be finished this way, without guessing.

The rules

Thick lines split the grid into regions of one to five squares. A region of two squares holds 1 and 2, a region of three holds 1, 2 and 3, and so on. Two squares that touch, side by side or only by a corner, never hold the same digit. That second rule does most of the work.

Step 1: one-square regions and full neighbours

A region of one square holds 1, always. A region of two squares next to a 1 that touches both its squares cannot use 1 in either of them: wherever its 1 goes, it would touch the other 1. Look for these first.

Step 2: the only digit a square can take

For an empty square, list the digits its region still needs, then cross out every digit written in the eight squares around it. When one digit is left, write it. Notes make this easy: pencil in the candidates, rub them out as the neighbours fill in.

Step 3: the only place for a digit

Turn it around: take a digit the region still needs and look for the squares that can hold it. If only one square of the region is not touching that digit somewhere, the digit goes there.

Step 4: squares a digit cannot avoid

Sometimes a region's 4 can only go in two squares, and both of them touch the same outside square. Wherever the 4 ends up, it touches that square: so that square cannot be a 4. This is the move medium and hard puzzles ask for.

Step 5: pairs

When two squares of a region can only hold the same two digits, those two digits are used up: no other square of the region can take them, and neither can a square outside that touches both. Hard puzzles sometimes need this.

The three levels

Easy: 5 by 5. Steps 1 to 3 are enough.
Medium: 6 by 6. Step 4 is usually needed.
Hard: 8 by 8, a big grid where step 4 comes up again and again, and sometimes step 5.