I know, the title is something of a come-on, isn’t it? But according to the free (tipware), cross-platform Sudoku Susser, if you’re going to get to grips with the harder sudokus (such as those in the “difficult” category of thelondonwastepaper - which is the only part of that paper I read, apart from the cartoons on the opposite page, and the only reason I read those is to marvel at the fact that they’re still going despite being dire) then you need to understand the concepts of “naked pairs”, “naked triplets” and even “X-wings” - the latter, it seems, a subset of fishy cycles, which apparently are “hard to explain”.
Reading the manual for this program was like stepping into a deep pool: you suddenly realise that there are people out there who are into this topic in a much, much deeper way than you would ever find (a) time for (b) the interest for. Kind of a mini-version of any specialist subject online, really.
Naked pairs and naked triplets (since you’re wondering) are unsolved squares - respectively two and three - which can only have, respectively, two or three possible numbers in them. So those numbers are ‘locked out’ from other numbers in their associated square/row/column. It’s a probability-reducing thing. And you thought it was something you’d find in the Sunday Sport.
And before we deal with fishy cycles, we must (like something out of Lewis Carroll) consider the Swordfish:
The next step up in complexity from an X-Wing is a Swordfish pattern. Instead of looking for a 2×2 set of rows and columns, Swordfish uses a 3×3 set.
Apparently “fishy cycles” - which are something to do with interrelationships between unsolved sudoku squares - are discussed here - though I’m not sure that’ll clarify much.
Anyhow, if you’ve had sudokus that have driven you mad and you’ve been sure that they’re insoluble or have duplicate solutions, this program will give you the lowdown. And the price (though remember, it’s tipware) is hard to beat. Even though the graphics are a bit mind-boggling.