5️⃣ Suguru
🧩 Logic · 1 playsSuguru
Fill each cage with the digits one to its size, letting no equal digits touch.
About Suguru
Also known as Tectonic, this puzzle divides the grid into cages of varying sizes. A cage of five cells takes the digits one to five, a cage of three takes one to three, and each digit appears once per cage — while across the whole board, no two equal digits may sit in touching cells, diagonals included. There are no rows or columns to scan; the adjacency rule does all the work that rows do in sudoku, and it works harder. A single placed digit clears its value from up to eight neighbours, so the deductions ripple outward in a way sudoku solvers find pleasantly unfamiliar.
How to Play
Each bold cage of N cells takes the digits 1 to N, each exactly once. No two identical digits may touch anywhere on the board, not even diagonally. Select a cell and enter a digit, using notes for candidates while you work.
💡 Tips & Strategy
Start with the largest cage and the cells with the most neighbours in other cages. A five-cell cage must hold a 5, and in a snaking cage the 5's possible homes are few; each candidate placement sprays exclusions across up to eight touching cells, so testing them is cheap and profitable.
Think of each digit as radiating a forbidden zone. Two identical digits may not touch even diagonally, so a placed 4 clears 4 from every surrounding cell — and where two cages interlock, a digit forced somewhere within one cage can eliminate that digit from cells of the neighbouring cage even before its exact position is known. If every possible home for the 3 in one cage touches a particular outside cell, that cell cannot be 3. This shared-neighbour argument is suguru's version of the pointing pair, and it breaks most hard positions.
Small cages are gifts. A one-cell cage is a given 1, and its ripples are immediate. A two-cell cage holds 1 and 2 in some order; whichever cells outside touch both of its cells can hold neither 1 nor 2.
Count within the cage before you look outside it. Each cage holds 1 to N exactly once, so a cage with one empty cell is finished arithmetic, and a cage where the 2 has only one non-touching-another-2 home is done reasoning. Alternate cage-counting with the adjacency sweep; when both stall, find the cell with the fewest candidates and examine what each candidate does to its neighbours — one of them nearly always contradicts within two steps.