Sudoku medium difficulty help

Sometimes you have to look at rows and columns which have more than 3 empty spaces left! Consider the space on the third row between the 6 and 2...

Your strategy should work for most sudokus if you don't limit yourself in this arbitrary way. Consider ALL rows and ALL columns, even if they have 4 or more empty squares, and you should find places you can make progress, like in my example above. Good luck!

Spoiling all the candidates in the attached image, but useful tool that can help you with hints, and the strategy behind the hint: https://www.sudoku-solutions.com/index.php?page=sudoku9by9

I think it usually gives you the easiest hints first, and then more and more complex strategies as needed.

When you find rows and columns that have only three boxes left you fill those numbers in (green in the image). Switch contexts and realize you now have only three empty boxes in the top-right square.

Sometimes you need to look not only to separate numbers, rows and columns, but also the whole rows and columns of 3x3 blocks. In your example, you can notice that in top right 3x3 square, number 7 can be only in the top row. This cancels the possibility of number 7 being in the first row in the left block, leaving the number 9 the only option in the top left corner.

Starting with the givens in the original puzzle (not taking your eliminations into account) and after propagating the obvious constraints from the givens, the puzzle is solved with:

• a hidden-single-in-a-column (==> r3c1 = 8),

• followed by two interactions between rows and blocks (the most elementary rules after singles):

5 in row r9 ==> r7c2 ≠ 5

6 in row r5 ==> r4c8 ≠ 6, r4c7 ≠ 6

• followed by singles