The Opening Cross-Hatch & Snyder Sweep
Never start by writing notes in all 81 squares—this leads to cognitive visual overload. Begin with a fast cross-hatching sweep for digits appearing 5 or more times. When noting possibilities, employ Snyder Notation: only write pencil marks in cells where a number can fit in exactly two positions inside a 3×3 box.
Mastering Pointing Pairs & Triples
This is the signature technique that unlocks 60% of hard bottlenecks. When all candidate notes for a digit inside a 3×3 box align on the same horizontal row or vertical column:
The Deduction Rule:
That digit is physically locked into that 3×3 block’s row. Therefore, it cannot exist anywhere else in that entire row outside the box. Erase candidate notes in that line across the other two boxes immediately!
Box-Line Reduction (Claiming Candidates)
The inverse of pointing pairs: when a candidate digit in a row or column is confined strictly to a single 3×3 box, that block "claims" the digit. You can safely eliminate that digit from all other empty squares inside that 3×3 block.
Naked Pairs and Hidden Pairs
When two squares in the same row, column, or block contain strictly the identical two candidate options (for example, [4, 9] and [4, 9]), those two digits are completely locked into those two cells. Neither 4 nor 9 can go anywhere else in that unit.
The Middle-Game X-Wing
When subsets are exhausted in the middle-game, search for an X-Wing: two parallel rows where a digit only appears in the exact same two column positions, forming a rectangle. This eliminates candidate instances in those columns across the rest of the board.
Put These Strategies to the Test!
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