Suguru Techniques: Five Steps from Stuck to Solved
Suguru hides a complete logic course inside two rules. Fill each bold-outlined cage of N cells with the numbers 1 to N, each exactly once, and never let two identical numbers touch, not even diagonally. That's the whole game, usually credited to the Japanese puzzle inventor Naoki Inaba and sold across European newspapers as Tectonic. No math, no arithmetic, and, on a fair grid like the ones our Suguru generates, never a guess: every puzzle has exactly one solution reachable by reasoning alone. When you're stuck, you're not out of luck, you're missing one of five moves. Here they are, in the order they usually break a puzzle open.
1. Harvest the free squares
A one-cell cage holds a 1, always, before you think about anything else. Mark every one of them first, because each placed number radiates a ban into up to eight neighbors, and those bans are the fuel every later step burns. In the same pass, note each cage's ceiling: a three-cell cage will never contain a 4 or 5, which sounds obvious and quietly kills half the candidates on the board.
2. Let the neighbor ban do the counting
The touching rule is the puzzle's engine, and its basic use is subtraction. Take a five-cell cage snaking past a placed 3: any of its cells that touches that 3, straight or diagonally, cannot be the cage's 3, and if only one cell of the cage escapes the 3's shadow, that cell is the 3, done. This is the bread-and-butter deduction of Suguru, and the discipline is to run it number by number, not cell by cell: pick a digit, shade every square that digit is banned from, and watch a cage collapse to one legal home for it.
3. Find the pinch points
Two cells of the same cage that sit diagonally adjacent to one shared outside square make that square a pinch: whatever pair of numbers the two cage cells eventually hold, the pinched square touches both, so it can hold neither. The pattern generalizes: any outside square touching K cells of a cage is banned from every number those K cells could hold as a set. Spotting pinches is the difference between intermediate and fast solvers, because a single pinch often bans two or three digits from a square at once, and a square reduced to one candidate is a solved square regardless of its own cage's state.
4. Push pressure across cage borders
The expert move is reasoning about where a number must go rather than where it can't. If every legal home for the 4 in cage A happens to touch a particular cell of cage B, that cell of B can never be a 4, even though you don't yet know which cell of A holds it. This is the same style of inference as the pointing pairs in Sudoku solving, translated from rows and boxes into geography, and it's the move that cracks the last third of a hard grid, when the easy subtraction has run dry. Slow down, pick the most-placed number on the board, and trace its remaining homes cage by cage.
What makes a hard grid hard
Every Suguru uses the same five moves; difficulty is about how much of the work each move can do. Easy grids hand you several one-cell cages and a sprinkle of given numbers, so step one and step two carry you most of the way. Hard grids are stingy: few or no free squares, big five-cell cages whose candidates stay wide open, and givens placed where their bans overlap instead of spreading. That pushes the weight onto pinch points and cross-cage pressure, the two moves that need real looking, which is the entire difference you feel between a two-minute grid and a fifteen-minute one. If a hard puzzle stalls, the stall is nearly always in step four: some number on the board has exactly two or three remaining homes in a cage, and their combined shadow is the ban you have not drawn yet.
5. Sweep the endgame
Late Suguru plays itself if you let it: every placement bans neighbors, every ban shrinks a cage, every shrunk cage places another number. When a chain like that starts, ride it to the end before returning to analysis. If the chain stalls with the puzzle unfinished, resist the temptation to try a number and see: return to step three, because in a well-made grid there is always another pinch, and finding it is the actual game. Guessing solves the grid and skips the puzzle.
The habits transfer well. Sudoku is the same candidate-pruning discipline with arithmetic-free constraints of its own, Nonogram swaps number bans for line-counting, and Star Battle is practically Suguru's sibling, adjacency ban included. All of them live with the rest of the logic puzzles, free in the browser, with fresh solver-verified grids whenever you want them. Five moves, two rules, no guessing. That's the entire toolkit, and it never gets old to use.