Very Hard Sudoku

Very hard and expert are the same band on this site

Worth saying plainly rather than implying otherwise. The engine recognises four grades, named after the hardest deduction each one forces, and this page and the expert page both request the top one. Calling a sudoku very hard rather than expert is a difference of wording, because people look for both, and not a fifth grade hidden behind one of the two names. Where the pages differ is what is written around the board, and the material below is what this one is for.

Difficulty labels do not travel between websites

There is no standard scale. One publisher’s hardest tier is another’s middle, a newspaper’s Saturday grid and a puzzle book’s five-star grid have no relationship at all, and none of them are lying – they are simply measuring different things, when they are measuring anything. Some grade by clue count, some by how long a test solver took, some by a rating their software emits with no published meaning. The only useful question about a label is what it was defined against. On this site it is defined against a list of six named deductions, and the grade is the hardest one the board could not avoid.

The clue count myth, measured

The belief is that a harder puzzle shows you fewer digits. It is easy to test here, because the generator can be asked for each grade in turn. Eight boards were taken at each of the four grades and their givens counted:

Grade requested	Given digits, lowest to highest
Easy	24 to 27
Medium	24 to 26
Hard	23 to 26
Expert	24 to 26

The four ranges sit on top of each other, and the sparsest board in the whole sample – twenty-three givens – came from the hard request rather than the top one. This is not an accident of the sample. The generator digs holes for as long as the solution stays unique and the puzzle stays no harder than requested, so it stops for a reason that has nothing to do with how many digits are left. A grid that falls to plain scanning with thirty clues is easier than one needing a triple with thirty-four, and counting blanks cannot see the difference.

What a genuinely harder puzzle would need

Above the deductions used here sit techniques that follow implications rather than eliminate within a unit: chains that hop from cell to cell on the strength of if-this-then-that, colouring, and the various forcing arguments. They are legitimate, people enjoy them, and they are deliberately outside what this generator will produce, because the moment a puzzle needs one the grading claim stops being checkable against the solver that made it. The line between a very hard puzzle and a puzzle that needs guessing is thinner than it looks, and this side of it is the side worth being on.

If this board is not resisting

Difficulty is partly what you have practised, and a very hard sudoku is only very hard until the deduction it turns on becomes familiar. Someone who spots naked pairs fluently will find this grade merely brisk, and the way to make it bite again is to try it without pencil marks – scanning only, nothing written down. Alternatively, drop the grid size: a six-by-six board solved in your head is a different exercise from a nine-by-nine solved on paper.