Play Suguru Online
Fill every group with the numbers 1 to N so that no two identical digits touch — not even diagonally. A pure-logic number puzzle also known as Tectonic or Number Blocks.
Created by Brian Hamilton
How to play Suguru
Fill every square with a number. A group of k squares holds the numbers 1 to k, once each.
- No two equal numbers may touch — including diagonally.
- Rows and columns have no rule of their own. The same number may appear several times in a row, as long as the repeats do not touch.
- Groups here run from two to five squares, so 6 never appears.
- Every puzzle has exactly one solution.
Controls: tap a square and type or tap a number. Notes lets you pencil in candidates, and Check highlights mistakes.
Nothing on a Suguru board sees very far
Suguru looks like a Sudoku variant and is solved nothing like one. The difference is that its constraints are local: a number you write down affects the squares immediately around it and the group it sits in, and nothing else at all.
In Sudoku, placing a 7 rules that digit out of eight other squares in its row, eight in its column and the rest of its box — twenty squares strung right across the grid. In Suguru, placing a 3 rules 3 out of the eight squares touching it, plus the other squares of its own group. The rest of the row and the rest of the column are untouched.
This is why Suguru scales to sizes Sudoku never could. A 12×12 Suguru is not harder than a 6×6 — it is a longer sequence of small deductions. You are never holding the whole board in your head, only the patch you are working on. It also means that if you get stuck, the answer is always nearby: there is no such thing as a deduction that depends on the far corner.
Groups are small, and never larger than five
A group of k squares holds the numbers 1 to k, once each. So group size is the whole of the difficulty in a group: a two-square group is a coin flip between 1 and 2, and a five-square group has 120 orderings before any constraint applies.
Across 24 generated boards holding 300 groups, no group was ever smaller than two or larger than five, and every single board's largest group was exactly five. The number 6 never appears in this puzzle.
| Squares in group | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| Share of all groups | 14% | 14% | 31% | 41% |
| Numbers it holds | 1–2 | 1–3 | 1–4 | 1–5 |
Read the bottom row upwards and a technique appears. A 5 can only ever sit in a five-square group — 41% of groups. A 4 needs a group of four or more: 72%. A 1 or a 2 can go anywhere. The bigger the number, the fewer places on the board can hold it, which is the reverse of Sudoku, where every digit is equally common.
So hunt the high numbers first. If you need to place a 5, you are only ever looking at the five-square groups, and each of them contains exactly one. On a 6×6 board with nine groups, that is typically three or four groups to check rather than the whole grid.
A worked board
Begin at the two-square group. It holds a 1 and a 2 in some order, and whichever of its neighbours already carries a 1 or a 2 settles which way round. From there the diagonal rule does most of the work: each number you place removes a candidate from up to eight squares, and in groups of two or three that is usually enough to force the next one.
Where solvers get stuck
Forgetting the diagonals. This is the single commonest error, because every other grid puzzle trains you to look along rows and columns. Two equal numbers may not touch at a corner either. When you place a number, check all eight squares.
Looking for row and column constraints that do not exist. A row may contain the same number several times, as long as the repeats are not adjacent. People lose time trying to complete a row as though it were a Sudoku line. Rows and columns mean nothing here.
Starting with the big groups. A five-square group has the most freedom and tells you least. Work the twos and threes first — they are 28% of the groups and they are nearly self-solving.
Two things you can check about these puzzles
Every puzzle has exactly one solution. A board starts as a completely filled grid, and numbers are removed one at a time — each removal kept only if a solver confirms a single solution remains, and put straight back otherwise. Because no step that would create a second answer is ever accepted, ambiguity cannot appear. Boards at all four offered sizes were checked against a separate counter written from the rules alone; all 32 had exactly one solution.
Easy and Medium hold a fixed proportion of givens; Hard does not. After the removal pass, Easy is topped back up to 45% of the squares and Medium to 33%, so those settings are consistent. Hard keeps whatever the removal pass reached — measured at 17% on 6×6 and 9% on 8×8. That is why the jump to Hard feels so much larger than the jump from Easy to Medium: it is not a step in a scale, it is the removal running to exhaustion.
Suguru, Tectonic and Number Blocks
Suguru is credited to the Japanese puzzle designer Naoki Inaba, and appears under several names: Tectonic across much of Europe, and Number Blocks or Suguru in British papers.
Of the grid-and-number puzzles it is the most approachable, because it is the only one that subtracts a rule rather than adding one. KenKen adds arithmetic to a Latin square, Killer Sudoku adds cage sums on top of full Sudoku rules, and Futoshiki adds inequalities. Suguru drops the row and column constraints altogether and keeps only a touching rule, which is why it can be explained to a child in about thirty seconds.
More number-placement puzzles
If you like filling grids with digits, try these: