Advanced Suguru rules
Suguru, also called Tectonic, is a region puzzle. This page goes past the first explanation: how region size fixes a digit, how a single neighbour can empty a cell, and how to finish a hard grid without guessing.
The two rules
The grid is split into regions. A region of N cells contains each of the digits 1 through N exactly once. A region of one cell is always 1. A region of two cells is 1 and 2. There is no 3×3 box and no row-or-column rule of the Sudoku kind.
The second rule is touching. Two identical digits must not share a side or a corner. Every digit looks at all eight neighbours. A 4 placed in the middle of a cluster removes 4 from every cell around it, including cells that belong to other regions.
Start with the small regions
Place every 1-cell region immediately. Then look at 2-cell regions that touch another 2 or a given. If one cell of a pair already touches a 1, the other cell is the 1 and the touched cell is the 2. The same elimination works for a 3-cell region: list 1, 2 and 3, then cross out any digit a cell can see.
A region of five feels large until you notice that 5 can only sit in the cells that do not already touch a 5. Often that is one cell. Place the 5, and the region collapses to a four-cell problem you already know how to do.
Seeing the whole neighbourhood
When you are stuck, stop looking at the region and look at one high digit across the grid. Every 4 must be at least one cell away from every other 4, corner to corner. On a small grid the 4s form a loose net. If three 4s are placed, the last region that still needs a 4 may have only one legal cell.
The same net works for 3s and then for 2s. Low digits are more common, so they are weaker as a net and stronger as fillers once the high digits are in. Do not start a hard grid by hunting 1s. The 1s fall out when the larger digits have taken their seats.
A cell with one digit left
Write the candidates that survive both rules. If a cell has one candidate, place it. If a digit is missing from a region and only one cell of that region can still hold it, place it even if that cell has other candidates. That is the region’s hidden single.
If two cells in a region are the only homes for two digits, those digits cannot appear in the rest of the region. They also cannot appear in any neighbour that both cells touch. The second half is easy to miss and is where most hard Suguru deductions live.
Hard and expert grids
Hard Suguru keeps the regions irregular so that a digit’s neighbours belong to three or four regions at once. One placement can empty a cell you were not looking at. After each digit, scan the eight cells around it before you hunt for a new region.
Expert grids rarely give a one-cell region next to the action. The opening is usually a high digit with a single legal cell, found by counting the cells a region can still use after the digits already on the board. If you are about to try two options, you have skipped a neighbour. Go back to the last high digit and list its eight cells again.
What this is not
Suguru does not ask rows or columns to contain each digit once. A row may hold two 1s if they do not touch, even at a corner. Players who import the Sudoku rule invent contradictions that are not in the puzzle.
There is also no arithmetic. Region size is the only total that matters: N cells, digits 1 to N, no repeats, and no equal digits touching. The daily puzzle on this site uses those rules and no others.