Solutions to hard puzzles, eg easter monster, that I've seen are often obscure and useful only to that puzzle. What I'm proposing is a general method that can be used to solve any puzzle. The method can be applied to single digits, units, or patterns, and the latter is most powerful. The method relies on testing each possible pattern for a digit to see if it leads to a contradiction.

I first encountered the concept of eliminating by contradiction when I studied discontinuous nice loops, a seemilgly well accepted technique. I then realized that solvers such as SE relied heavily on contradiction when getting into the 9.5+ range. However, there is no logical reason why one should be confined to testing single digits for contradictions - why not test a unit or pattern? The methodology for identifying contradictions is fully explained at my online solver (see below)

For a chosen digit, all patterns are generated, and one pattern at a time, the 9 members of the pattern are postulated to be true. A forcing net is then generated, and if a contradiction results then that pattern is removed from the total. After all patterns have been tested, the remainder are transformed into a 9x9 grid and compared to the actual Sudoku. If there is a cell that all remaining patterns include, then that cell can have the value of the chosen digit. If there are cell(s) which none of the remaining patterns pass through, then the digit can be removed from these cell(s).

The Killer Method

If the above is not enough (as is the case in the very hardest puzzles) some something extra is needed. If one generates an array of all instances of a digit occurring twice in a unit (ie pairs), then one can make one of the pair true, then a pattern to be true, and see if there is a contradiction. If there is, then can make the other of the pair true, and the same pattern true, and if there is again a contradiction, then the pattern must be false and can be eliminated. This is because one of the pair has to be true, so the contradiction must be due to the pattern. This process can be enabled for triples and even quads. (in very hard puzzles there arenâ€™t many pairs, so triples are initially needed). The progress of this method is fully outputted into a text box so the logic can be examined.

This new method, along with the similar one for single digits and units can be tested on my new online javascript solver at http://www.philsfolly.net.au