sudoku techniques — Gridmark

Every sudoku can be solved with nothing but careful elimination. The difference between an Easy puzzle and a Hard one is which techniques you must reach for. Here they are, in the order Gridmark’s own difficulty grader applies them.

Naked single

A naked single is a cell that can hold exactly one digit, because the other eight digits already appear somewhere in its row, column, or 3×3 box. Scan a cell, cross off the digits you can see around it, and if only one candidate remains, that digit is forced. Naked singles are the workhorse of Easy puzzles — a grid solvable with them alone needs nothing more.

Hidden single

A hidden single is the mirror image: a digit that can go in only one cell of a unit, even though that cell still shows several candidates. Look at a single row, column, or box and ask, “where can the 7 go?” If the answer is one cell, the 7 goes there. Hidden singles are slightly subtler than naked singles and are still an Easy-tier technique.

Naked pair

When two cells in the same unit contain the exact same two candidates — and no others — those two digits must occupy those two cells, in some order. That lets you remove both digits from every other cell in the unit. Naked pairs are the entry point to Medium difficulty.

Hidden pair

A hidden pair is two digits that appear as candidates in only two cells of a unit, hiding among those cells’ other candidates. Because those two digits are confined to those two cells, every other candidate in those cells can be erased. Hidden pairs are harder to spot than naked pairs — finding them is the top of Medium tier.

Pointing and claiming

These two “box-line reduction” tricks share one idea: when a digit’s positions in a box all lie on one row or column, that digit cannot appear elsewhere in that row or column. Pointing works from a box outward; claiming works from a line inward. Both are the first genuinely Hard techniques in Gridmark’s ladder.

X-wing

An X-wing forms when a digit appears in exactly two cells of two rows, and those four cells also share the same two columns. The digit must occupy opposite corners, so it can be eliminated from the rest of those two columns. X-wings (and their larger cousins, swordfish) are the floor of Gridmark’s Expert tier: an Expert puzzle can never be finished without at least one fish or the chain that follows it.

Forcing chain

When every simpler technique stalls, a forcing chain is the last honest step. Pick a cell with two candidates and follow the consequences of each: “if this is a 4, then that cell is a 7, which forces…” If both branches drive the same cell to the same digit, that digit is settled no matter which branch is true — a real deduction, not a guess, because you never had to commit to either branch. Forcing chains are the top of the ladder and the defining requirement of every Expert puzzle Gridmark generates. They demand patience and a clear head; solve one clean and you have solved the hardest sudoku logic there is.