# Sudoku-X and the diagonal challenge

One of the perennial comments on PuzzleMix is that the diagonal ‘X’ regions aren’t needed in a particular Sudoku-X puzzle, or more commonly in Killer Sudoku X. Well, when I say “perennial” I mean to say that of the more than 400,000 puzzle plays that that comment has been made about 10 times. But an interesting point nonetheless.

Obviously a regular Sudoku has 9 rows, 9 columns and 9 boxes. Are we annoyed if we don’t “need” all 27 regions? Probably not. But in an ‘X’ puzzle I suppose it’s understandable that you’d expect to use the ‘X’.

Now of course there are different definitions of “needing” a region. Strictly-speaking, if you can prove a unique solution via any method (e.g. recursive search) without the regions then you don’t need them. But I decided to define “need” as meaning “you can’t solve the puzzle without them whilst using the standard solving techniques”. Standard techniques are those that Nikoli allow, so everything up to x-wings and hidden/naked quads.

Using this definition I looked at 100 randomly-selected Sudoku X puzzles of mine and found that 98 “needed” the diagonals, and only 2 didn’t. Not bad! Of course this result will vary depending upon how vigorously you prune the number of ‘given’ digits in a puzzle.

It’s worth noting that not “needing” a region does not preclude it being useful – for example an easy Sudoku-X puzzle may happen to also be a very difficult regular Sudoku, so there is still value in including the regions even if they aren’t strictly-speaking essential. However there are enough Sudoku puzzle possibilities in the world that we can ignore this and simply select puzzles that don’t have any ambiguities.

So to celebrate, here’s a Sudoku X to solve. Just place 1-9 in each row, column, 3×3 box and the two main diagonals… but you know that already!

Next time I will look at Killer Sudoku X, but with the much heavier constraint of all the extra Killer regions I imagine the X will be needed far less of the time, thus the PuzzleMix comments. So I will be filtering my puzzles in future to make sure the X is always needed! I’ll also be filtering them for extra regions puzzles to make sure those are essential to solving them too.

Mind you, at the end of the day some people always find some puzzles easier than average just by making a fortuitous error – I’m sure we’ve all done it without realising! At those times there will always be puzzles that don’t seem to “need” the X…

Spittledungabout 9 years ago

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Well you definitely need the X for THIS one!

I am curious about the way people started solving this puzzle. Hands up how many people immediately found the 7 in the middle region and started solving the 7s?

I like the X-factor because it adds new ways to solve a puzzle even if you don’t need the X. I enjoyed finding the Y-wing made of 8s in the X section and that wouldn’t have happened without the X constraint. Also, the X made a few X-wings in the lower regions that were fun to find,

I usually don’t get DELL puzzle books (although I like their cross sums / kakuro), but I did pick up an Extreme Sudoku book and do the X-factor sudokus in it when I feel the desire.

about 9 years ago

Out of interest, have you noticed if the Dell ‘X’ puzzles always ‘require’ the X?

Spittledungabout 9 years ago

Hmmmm. I didn’t try to do them without the X. I mainly did them to practice Y-Wing hunting. Next time I do some of the easy puzzles in the book I’ll try and overlook the X and see what happens.