Last Saturday (04/02/2017) the UK's Guardian news paper offered its puzzle No 3663 (https://www.theguardian.com/lifeandstyle/2017/feb/03/sudoku-3663-hard). I got stuck about half way through.
Here is an image of the sticking point. Essentially, the bottom row of the grid needs only 3 cells to complete, but none of my standard techniques work. I resort to arguing that in the 4th column two of the empty cells are limited to two possible answers (1 or 6). In effect the answers in these two cells (circled in red) are mutually exclusive and cannot appear anywhere else in the column. Since the only available answers to the 9th row are 1, 6 and 8 (see the green ellipse) and 1 and 6 are taken, the only possible solution for cell 8_49 (see Grid Nomenclature) is value 8.
Is there a better argument?