# Puzzlemix

## iPad, iPhone and other touch support on PuzzleMix

Just a quick heads-up that PuzzleMix, my site where you can play a wide range of puzzles online, now supports touch screen play for all of the number entry puzzles – so that’s Sudoku, Killer Sudoku, Futoshiki, Calcudoku, Skyscraper, Sudoku X, Kropki Sudoku, Killer Sudoku Pro, Jigsaw Sudoku, Consecutive Sudoku, Wraparound Sudoku, Sudoku XV, Killer Sudoku X, Odd Pair Sudoku and more.

It’s pretty darn awesome, even if I do say so myself!  It handles the screen touch events directly so it’s just as fast as running a native application on the iPad or iPhone. It also works on other devices.

## Solution time distribution graphs

I was tidying my desk earlier when I suddenly thought: wouldn’t it be fun to see exactly how your puzzle solving time compared with every other solver?!

And so now you can. If you play puzzles online at PuzzleMix then the statistics show a distribution of solution times, highlighting where you fitted:

My result is the yellow/pale blue bar, and as you can see I was the second or third fastest on this particular puzzle.  Previously all I’d have known is that I was better than average, and near the fastest. Now I can see just exactly where I fit in.

I think this is great! Of course, it’s a bit embarrassing when your highlight bar is off to the right, or doesn’t even fit on… (it only shows the top 90% of results when there are 20 or more, and omits all results longer than 2 hours).

## Killer Sudoku-X

I wrote quite a lot yesterday about whether you “needed” the X in some Sudoku-X puzzles. I promised that I’d follow up with the result of analysing a stack of Killer Sudoku-X puzzles, and so here is that result.

I picked 64 Killer Sudoku-X puzzles (52 for the daily puzzlemix section plus 12 for the weekly puzzlemix section), and of those about 5 or 6 (I didn’t write it down…) could be solved via reasonable logical deduction without using the ‘X’ diagonals.  So that’s roughly 10% of puzzles, if picked at random, that don’t need it.  Quite a bit worse than regular Sudoku-X (see previous post), but nowhere near as high a percentage as I’d expected – I had thought it could be 50% or more, although I should say that this isn’t actually a fair comparison because I disabled the cleverest maths-solving techniques from my analysis software. So in fact this is comparing clever Sudoku-X solving against the same Sudoku-X solving with the addition of relatively less clever Killer Sudoku-X solving, so perhaps this biased the result much more to the non-Killer result (from yesterday) than it should have done.  But anyway, I’m not writing a scientific paper and it’s good enough for me!

Killer Sudoku-X puzzle
So the result of all this is pretty simple: the Killer Sudoku-X on PuzzleMix for the coming year should be better than ever!  You should need that X every time…

PS Enjoy the Killer Sudoku-X I’ve attached here! Just place 1 to 9 in each row, column, 3×3 box and main diagonal, plus make sure the cages add to the given amounts – and don’t repeat a number in a cage.

## 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.

Sudoku-X puzzle

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…