Sudoku

Hard sudoku is where pair-based techniques become essential. Naked pairs, hidden pairs, and occasionally triples — these are the tools that separate hard from medium. If you haven't encountered them before, the strategy guide walks through each one with examples.

Full candidate lists are worth the effort at this level. Write down every possible number for every empty cell, then scan those lists for patterns. Two cells in the same row both have only {3, 8} as candidates? That's a naked pair — remove 3 and 8 from every other cell in that row. Those eliminations often cascade: removing a candidate from one cell creates a naked single in another, which then reveals a hidden single in a third. One good pair identification can unravel half the grid.

Hard puzzles give you roughly 24 to 28 clues. The grid looks sparse when you start, and the first few minutes are usually just scanning and filling in candidates. Don't rush this part — accurate pencil marks are everything here. A single missed candidate will make every advanced technique fail, and you'll end up second-guessing correct deductions.

Every puzzle at this level is solvable without guessing. If something feels like a coin flip, there's a pair or triple you haven't spotted yet. Hard sudoku is where most players find their sweet spot — complex enough to be satisfying, but not so dense that you need to track five techniques at once. Enjoy the challenge.