Suguru solving techniques

These are the six moves my puzzle generator knows. It solves every daily puzzle the way a careful person would, always reaching for the easiest move that works, and the hardest move it needed decides how difficult the puzzle is. So this page doubles as a map of the week.

You might know the puzzle as Tectonic or Number Blocks; the moves are the same whatever it's called. If you've never played, start with the beginners' guide.

Which moves you'll need, day by day

Monday and Tuesday only ever need the first two.
Wednesday, Thursday and Sunday can need anything up to number 5.
Friday and Saturday can need all six.

The generator checks this for every puzzle, so a Wednesday can always be finished with techniques 1 to 5. If one has you stuck, the move you need is somewhere on this page.

How to read the pictures

Each example is a small board, drawn the same way as the game. I've left out any numbers that don't matter for the step, so they look emptier than a real puzzle would.

A number already on the board.
The number this step works out.
Circled or ringed: the reason for the step.
Hatched: the number in question can’t go here.
Notes, the small pencil marks for what a cell could still be. Red ones have just been ruled out.

I call the outlined shapes blocks. Some books and apps call them cages or regions. Two cells touch if they share a side or a corner.

1. The only number left

Also called a naked single

Pick an empty cell and ask what it could be. Its block sets the limit: in a block of 5, it's 1 to 5. Cross off every number already in the block, then every number touching the cell, corners included. If one number survives, that's the answer.

142153

The yellow cell's block already has its 4 and 5. The 1 above it and the 3 on its corner take care of 1 and 3. That leaves 2.

Most numbers in most puzzles go in this way. When a cell seems to have two options, check its corners before anything else. Diagonals are by far the easiest thing to miss.

2. The only place left

Also called a hidden single

Now turn the question round. Pick a block and a number it still needs, and ask where that number can go.

The block along the top needs a 1. The circled 1 below touches four of its five cells, so there's only one place left for it.

On its own, the yellow cell could be anything from 1 to 5. You'd never find this by staring at the cell. You find it by staring at the block.

1s are the best numbers to hunt with. Every block has one, so the board is full of them, and each one rules out up to eight cells around it.

3. Shared neighbours

Also called pointing

Sometimes you can't place a block's number, but you can narrow it down to two or three cells. That's still worth something. A cell outside the block that touches all of them can't hold that number, because wherever the number ends up, it'll be touching.

1411211

The block with the 4 in it needs a 1. It can't go in the hatched cell, which touches the 1, so it's in one of the three ringed cells (I've pencilled a 1 in each). The yellow cell touches all three, so it isn't a 1. It's in a block of 2, so it's a 2, and the cell above it gets the 1.

This is the first of the medium techniques, and my favourite of the six. Sudoku has something like it, but in Suguru it works round corners, and spotting one still feels like a small win.

4. Pairs

Also called a naked pair

Two cells that touch, or share a block, can never hold the same number. So if two such cells are both down to the same two options, say 1 or 4, one of them is the 1 and the other is the 4. You don't know which way round yet, and you don't need to: a cell that touches or shares a block with both of them can't be either.

314124214

The 3 and the 2 on the left leave the two ringed cells with 1 or 4 each. The yellow cell shares a block with one and touches the other, so it can't be 1 or 4. Its block already has the 3, so it's the 2.

In sudoku a pair sits inside one row, column or box. In Suguru the two cells can be in different blocks, like these, as long as they touch. That's the version people miss.

Triples work the same way with three cells and three numbers. They only turn up in the hard puzzles, and not often.

5. Hidden pairs

Also called a hidden pair

A pair turned inside out. If two numbers a block still needs can only go in the same two cells, those two cells belong to them, and anything else pencilled in there can go.

12341351233453454452331

This block still needs all of 1 to 5. The circled numbers on the right keep 1 and 2 out of its three right-hand cells, so the 1 and the 2 must fill the two yellow cells. Cross the 3 and 4 out of those. Now they're a pair, and technique 4 takes over.

Hidden pairs are the hardest of the six to spot, for me anyway. What helps is going block by block with notes on and asking each missing number where it can go. When two numbers give the same answer, you've found one.

6. What if?

Also called forcing, or a forcing chain

On a Friday or Saturday you'll sometimes run out of everything above. Then find a cell with just two options, pencil one of them in, and follow what it forces using techniques 1 and 2. If you hit something impossible, like a block with nowhere left for a number, the option you pencilled in was wrong, and the other one is right.

1234123454511234512352323254131

A real position from a 5×5 hard puzzle, with every easier move used up. The yellow cell is 2 or 4. Its block holds 1 to 4, but the block beside it has to put its 1 and its 3 in one of the three ringed cells, and the yellow cell touches all three.

Why can't that block's 1 or 3 go anywhere else? Its bottom cell touches the 1 and the 3 below it. Its top-right cell touches a 1, and it can't be a 3 either, because the block underneath has to put its 2 and 3 in the two cells just below it. That's technique 3 twice, which is typical of a hard puzzle: by the time you need a what-if, your notes are doing a lot of quiet work.

Say it’s a 4

414131

Nowhere for a 4

4414131

Say it's a 4. The block beside it can't put its own 4 anywhere touching that one, or next to the circled 4 below, which leaves a single cell. Between them, those two 4s touch every empty cell of the top block, so the top block has nowhere for its 4. The yellow cell isn't a 4. It's a 2.

This isn't guessing. A guess is writing a number in and hoping. A what-if is a small proof: you follow it until it breaks, and then you know. If it hasn't broken after a few steps, rub it out and try another cell. The what-ifs the generator allows only ever need techniques 1 and 2 along the way, so you can hold them in your head, or in notes.

A what-if is often the long way round to a pattern you haven't spotted. That's fine. Nobody's marking you on style.

Two shortcuts

Every 2×2 square holds four different numbers

Each cell of a 2×2 square touches the other three. So if a block of 2 sits inside one, it holds the 1 and the 2, and the square's other two cells must be 3 or more.

A cell that touches a whole block can't share its numbers

If a cell touches all three cells of a block of 3, it can't be 1, 2 or 3, whatever order they end up in. Small blocks tucked in beside a single cell are worth a look.

Both are technique 3 in a form you can see at a glance, before you've pencilled in a thing.

Where to practise

Monday's puzzle is the place to make the first two moves automatic. Wednesday is good for shared neighbours and pairs. Save the what-ifs for Saturday's 8×8.

More guides

Suguru for beginners
The two rules, the mistake nearly everyone makes at first, and a small puzzle solved one step at a time.
Suguru vs sudoku
What carries over from sudoku, what doesn’t, and why the two feel so different to solve.

Play today's puzzle Try the practice puzzle