Expert Killer Sudoku
The step from hard to expert is not more arithmetic. It is learning to make a move that places nothing: an elimination that removes a candidate somewhere and leaves the board looking exactly as stuck as it did before, until the next pass turns up the single it uncovered.
The move that fills nothing
Every technique below this level ends with a digit written into a cell, which is why they feel like progress. The six that define the top grade here do not. They take a candidate away from a cell that was never going to hold it, and the payoff arrives one or two passes later when some other cell is suddenly down to one option. Beginners give up on these precisely because nothing visible happens when they work.
The six
A pointing pair: if inside one box every remaining home for the 4 lies in the same row, then the 4 is somewhere in that stretch of row, so it can be struck out of the rest of that row beyond the box. A box line is the mirror of it: if every home for the 4 along a whole row falls inside one box, the 4 leaves the rest of that box.
A naked pair: two cells in the same unit that each hold the same two candidates and nothing else. Between them they will use both digits, so both digits leave every other cell of that unit. A naked triple is the same argument across three cells and three digits, which need not each show all three. A hidden pair inverts it: two digits which between them have only two possible cells left, which lets you delete everything else from those two cells.
And a region sum, which is the rule of 45 stretched past a single unit. Two rows hold 90 between them and three rows hold 135. When the cages covering such a band stick out of it by exactly one cell, or leave exactly one cell of it uncovered, that cell is the difference. A band three rows deep catches layouts that no single row ever would.
Why the badge sometimes says hard
A killer sudoku expert board is found, not manufactured. A layout with more than one answer gets one split and nothing more, because patching means splitting a cage, splitting a cage prints another total, and another total makes the puzzle easier – so a layout still ambiguous after that single repair is thrown away rather than patched into shape. Most candidate layouts are therefore thrown away, and the generator is working against a budget of a couple of seconds so that the page does not sit there generating while you wait.
Ask for this level repeatedly and you will not get it every time. What you do get every time is a board with exactly one answer that was solved to the end by reasoning before it was offered to you. If the hardest technique the site knows is a naked triple, then the hardest puzzle it will hand you is one a naked triple finishes.
Pencil marks stop being optional
None of the six can be spotted without candidates written down in front of you. Each one asks where a digit is still allowed to sit, and an empty cell answers that question with nothing at all – the information is in the marks or it is nowhere. Turn Notes on, pencil the cage combinations into every cell before placing anything, and keep them current as you go. On a board at this level, maintaining the marks accurately is most of the work and the placements are the easy part.