Summary
Highlights
Instead of singles, look for pairs at the start. In a puzzle, a '58 hidden pair' in column five can restrict possibilities. Another example is a '59 hidden pair' in column three, which is crucial for advancing in harder puzzles.
After finding pairs, analyze their impact on the row, column, and block. The '59 pair' in column three restricts 'fours' in Block seven to a pointing pair. This then allows solving 'four' in Block four. Identify other pointing pairs like 'threes' in Block nine and 'fours' in Block five.
Marking potential locations for numbers, especially when a digit is restricted to two spots, helps identify opportunities. For example, 'eights' in Block one form a 'claiming pair' in row three, restricting where 'eights' can be placed elsewhere in that row.
Identifying digit restrictions can accelerate solving. For example, the '23 pair' in row seven, combined with other existing numbers, can lead to a 'naked single one'. This single 'one' can then trigger a chain of other solves throughout the grid.
When a cell has only two possible candidates, it's a 'bivalue cell'. Identify these cells to uncover advanced strategies. For instance, in row seven, the restriction of other numbers leads to a 'naked single four', helping to fill out '89 naked pairs'.
Further investigate areas with bivalue cells (BVCs). In Block eight, filling out columns reveals multiple BVCs. By observing how candidates are shared or interact, like with the '36' and '68' cells, you can find advanced patterns like an 'XY wing' to eliminate possibilities.
The final and most impactful tip is to systematically remove marks as solutions are found. These marks represent one and two-step restrictions, and quickly clearing them reduces clutter and reveals further solves. This allows for rapid completion of the puzzle.