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 puzzleSo 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.

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…

Killer Sudoku Jigsaw puzzle

I’ve recently been working on refreshing the content for PuzzleMix.com, my play-online puzzle site, and one of the puzzle types I’ve been making is Killer Jigsaw Sudoku, where you not only have the jigsaw-shaped Killer regions but also jigsaw shapes instead of the regular 3×3 Sudoku boxes.

So I thought it would be a good idea to post one of these puzzles here – they can be quite tricky, at least until you get your head around the difference between these and regular Killer!

The rules are simple:

• Place 1 to 9 in each row, column and bold-lined region
• Place numbers in the dashed-line cages that add up to the given total for that cage
• No number can be repeated in a dashed-line cage

Good luck!

Samurai-2 Odd Pair Sudoku puzzle

One of the brand new puzzles in Sudoku Xtra issue 4 is Odd-Pair Sudoku, which I wrote about last week here on my puzzle blog. As well as some regular 9×9 puzzles I also included a large 5-grid Odd-Pair Samurai puzzle, and to illustrate how the puzzle worked I included a small solved example alongside. A full 5-grid Samurai was too big to fit sensibly in the example box, so I made a 2-grid Samurai version just for that little solution area. So that’s the solution used, but what about the puzzle itself? Well, here it is! (And so if you want to check your solution – yes, it’s printed in Sudoku Xtra issue 4! Page 19, to be precise).

The rules, in case you missed them, are really simple:

• Place 1 to 9 in each row, column and bold-lined 3×3 box of the two 9×9 Sudoku grids
• Every pair of squares with an ‘o’ circle between them must sum to an odd value. (’o’ for odd). So for example you could have “3 o 6″, but not “3 o 5″ (since that would sum to 8, an even number).

This variant is fun because it eliminates lots of possibilities from squares relatively quickly, so you’re left with more deductive logic and less pencil-mark housekeeping.

Good luck!

Issue 4 of Sudoku Xtra magazine is now with us!  I really think I might be putting too many puzzles into it, because typing up the list of content just knocked me out with how much is crammed into its 52 large-format pages!  Is too much possible?  I don’t know, but look at this enormous list:

128 puzzles in total, including several seriously giant ones.  Brand new for this issue:

• Samurai Star Killer Sudoku Pro
• Number Link Samurai
• Odd Pair Sudoku
• Samurai Odd Pair Sudoku
• Sudoku Inequality Jigsaw
• Jigsaw Sudoku 6×6 Variety Pack (including toroidal, inequality, X, consecutive and killer)
• Killer Sudoku Pro Jigsaw
• Sudoku 15×15 and Sudoku 18×18
• Killer Sudoku 15×15
• Odd & Even Pair Sudoku
• Killer Sudoku Prime

Regulars from issue 3:

• Hanjie
• Masyu
• Calcudoku (three times as many as in previous issues!)
• Slitherlink
• Consecutive Sudoku
• Hitori
• Samurai Star
• Samurai Star Jigsaw
• Number Link
• Jigsaw Sudoku 8×8, 9×9 and 10×10
• Toroidal Sudoku and Toroidal Inequality
• Kakuro
• Futoshiki
• Killer Sudoku
• Skyscraper
• Skyscraper Sudoku
• Samurai Sudoku
• SSSS: Skyscraper Samurai Star Sudoku
• Sudoku Inequality
• Sudoku Extra Regions
• Jigsaw Sudoku Extra Regions
• Killer Sudoku Jigsaw
• SOS: Samurai Outside Sudoku
• Outside Sudoku
• Sudoku 8×8
• Sudoku 12×12 and 16×16
• Samurai Extra Regions
• Yajilin
• Nurikabe

Adding to that already exhausting list still further are the community puzzles: 

• Heyawake
• King’s Journey (also known as Hidato[TM], Numbrix[TM] and many other names)
• Mosaic (Minesweeper picture puzzle)
• As Easy as ABC
• Knight’s Tour
• Shapely Skyscraper
• Isolate
• Klump

And all of this for just £3.99 or $5.99 – it really is fantastic value!

If you’d like to get hold of it just pop on over to the Sudoku Xtra website!

Samurai 8-grid Calcudoku puzzle

Here’s probably the largest Calcudoku puzzle you’ve ever seen!  It’s made up of 8 underlying 9×9 grids, each of which must have 1 to 9 placed into each row and column, and then on top of this I’ve added the familiar Calcudoku regions.

For each Calcudoku region just place numbers such that the total after applying the stated operation between the numbers in the region is the one given.  For example, 7+ could be solved by 3 and 4 (3+4). For subtraction and division start with the largest number in the region, so 1- could also be solved with 3 and 4 (4-3).

Just to make it really clear, there are no 3×3 Sudoku box regions in this puzzle – just the 8 sets of rows and columns.

Good luck!

Sudoku Odd Pairs puzzle

Now here’s something I can guarantee you won’t have seen before, because I just invented it! Well, I suppose with a world of people creating Sudoku variants it’s possible there’s been something similar before, but I’ve bought a lot of puzzle magazines and books and never come across it, so perhaps I should say I can just about guarantee you won’t have seen it before!

So the puzzle is Sudoku Odd Pairs, and as the name implies it’s all about odd pairs of numbers. Now you may have come across regular odd/even Sudoku before, and to be honest it’s a pretty dull variant (which is why I’ve never made them) – in fact if you for example shade all squares that contain even numbers it just breaks into two separate puzzles that overlap, and if you instead mark just a selection of even (or odd) squares then it’s only interesting until you work out whether the shaded squares are odd or even.

Sudoku Odd Pairs isn’t like that, because instead of marking squares what I’ve done is mark pairs of squares. Some squares have a grey circle between them – you can think of this as an O for Odd. What this means is that the sum of the solution of these two squares is odd. I don’t mark all odd pairs, however, because if you do this you need only one single digit in the entire grid (any of the givens will do) to work out which squares are odd and which even and then you end up with the above boring variant again.  So this is important: you can’t infer anything about squares without an O between them – only those with the O between.

It turns out (at least in my opinion!) that this is actually a really fun variant, because you end up with many interesting parts of each puzzle where you realise you can force sets of odds or evens into groups of squares (and not just those with the Os on), which in turn effect the rest of the puzzle. You do to an extent need to make pencil marks when solving, as in Consecutive and many other variants, but the nature of the constraint is such that the number of pencil marks is roughly halved relative to most other variants which (for me at least) makes it far more fun.

I’ve talked about it enough. Try out the puzzle here and let me know what you think!

And if you would like more of these, I’m putting them into Sudoku Xtra issue 4 (out soon!), including a nice Samurai version.

Everything’s pretty much where it was before, but much shinier. I hope you like the new look!

Sudoku 36×36 puzzle

Giant Sudoku puzzles are one of those things that divide people.  With 25×25 puzzles some love them, whilst others simply can’t understand why anyone could ever have the patience to do them.  But whatever your personal opinion, they remain popular – even Nikoli (the people who named Sudoku ‘Sudoku’) make them regularly, and sometimes include them on special fold-out sections at the back of their books and magazines.

Since they are so divisive I try not to include many of them in Sudoku Xtra magazine (one of each, in fact, plus a 20×20). Therefore I recently created books of both 16×16 and 25×25 puzzles – available pre-printed or for download.  However what I’ve never tried making is a 36×36 puzzle – is there anyone, anywhere who would want to do one of these?  If so, let me know!

So just for fun, for those who would consider it fun, here’s a 36×36 Sudoku. Just place 1 to 36 into each row, column and 6×6 box. You’ll be relieved to know that no pencil marks are required to solve this puzzle!

Good luck!

Sudoku 15×15 puzzle

Something plain but unusual – a Sudoku 15×15.  I’m sure these must exist, but it occurred to me I’d never actually seen one.  So I made one.

The rules are as you’d expect: place 1 to 9 and A to F into each row, column and 5×3 bold-lined box.

There’s no need to make pencilmarks to solve this – scanning is sufficient.

If you try it out, good luck!

I’ve had lots of requests for a book like this over the past couple of years, so I hope if you’re one of the people who’ve wanted something like this that the book meets your expectations!  All of the puzzles have nice symmetry, and the difficulty level is set such that you won’t need to make lots of fiddly pencil marks in the grid (or indeed any pencil marks at all, if you don’t want to).

It’s printed on large paper (A4 at Lulu, 8″x10″ at Amazon), with just one puzzle per page, so you’re getting the puzzles at a comfortable size for solving. Full solutions are included, and with 50 puzzles it’s going to take you a long time to solve them all!

Please feel free to post any comments here, or head over to Sudoku Xtra and take a browse on the discussion forums – and maybe join in!

Right at the moment it’s only available in printed form, but I’ll have download copies available in the next couple of days – as soon as I’ve added a purchase mechanism to SudokuXtra.com in fact!

I’ve decided that I’m going to make a series of similar books of particular requested puzzles, all of which will be branded as “Sudoku Xtra Specials”.  In this way I can stay organised by keeping all of my download/printed content under the ‘Sudoku Xtra’ heading.  It means that you’ll always be able to find all of my new content in one place, without searching around my various sites.

This book is probably the nicest collection of 25×25 puzzles you can find, if you’re a fan of such things.  Every puzzle has really nice 8-way symmetry – having noticeable patterns in puzzles like this is pretty unusual, and it can help with the solve too.  Just as in my magazines, I’ve thought about what’s sensible in a puzzle like this so they can all be solved without needing pencilmarks.  How exactly would you go about making A-Y pencilmarks in each individual square anyway?!

If you get hold of it please do let me know any thoughts you have on it.  In the same way as for Sudoku Xtra magazine, it’s designed to be printed at home on either an all-together or a page-by-page basis.  And if you get a pre-printed version from Lulu or Amazon.com (already complete but waiting on listing now) then it’s on a large A4 (Lulu) or 8″x10″ (Amazon) page, so there’s plenty of room to write in the solutions.

If there are other books of puzzles you’d like to see, please let me know in the comments here or on the Sudoku Xtra forums – feel free to repeat any requests you’ve made before! Next up is 16×16 Sudoku but after that it’s all open. I was thinking of doing Inequality Sudoku third, but what do you think?

So if you’re in the US and fancy getting hold of a copy (they get really hard by the end!) then there’s now another way to buy it.  You even get 10% off if you’re a member.

Samurai Killer Calcudoku puzzle

I haven’t posted much here recently because I’ve been spending my time on Sudoku Xtra, so here’s a large puzzle to fill the void a bit.

This is a five-grid Samurai Killer Calcudoku:

• Place 1 to 9 into each row, column and 3×3 box of the five underlying 9×9 Sudoku grids
• Place numbers into the Calcudoku dashed-line cages to fulfil the results at the top-left of each cage.  The given operator when applied between all of the numbers must give the stated result, e.g. the solution to “5+” could be “2+1+2″. For subtraction and division start with the largest number, so for example “3-” could be “6-3″.
• Numbers can be repeated in Calcudoku cages, subject to the row, column and 3×3 box constraints.

Unlike my other puzzles I haven’t used any symmetry in this one, but I’m not sure it’s really that obvious on a puzzle like this one.  It’s not especially hard, but with so many places to potentially go it might take you a little while.

Good luck!

This issue is packed full of all sorts of puzzles, including SOS (Samurai Outside Sudoku!), Toroidal Inequalities and many more.  Community puzzles include picture puzzle Mosaic from Clarity Media, and some fantastic Slitherlink-Masyu cross-over puzzles called Shotgun Slitherlink from David Millar of The Griddle.  There’s also some brilliant Klump and Navigrid puzzles from Vexus Puzzle Design.

With 121 puzzles it will almost certainly take you far more than the month until issue 4 to complete, so you’d better get hold of it as soon as possible!

Pre-printed versions will be available in the next couple of days, but you can download and print it yourself immediately!

Outside Sudoku 6×6 puzzle

Here’s something new (for me at least) – an Outside Sudoku puzzle.  This one’s 6×6, just to get the ball rolling, but I have some larger ones (including some Samurai ones) ready for Sudoku Xtra issue 3!

The numbers outside the grid reveal some, none or all of the numbers that go somewhere in that same row or column anywhere up to the first bold line encountered – in other words, they go in that row/column of the adjacent bold-lined region.  If more than one number is given then the order need not necessarily be the same as that shown.

For example, look at the top-left.  The 4 and the 1 both go somewhere in the first three squares of the top row, but not necessarily in that order.  Below them the 6 goes in the first three squares of its row, and at the bottom-left of the puzzle the 4 and 5 go into the bottom two squares of the left-most column.

Then just follow through as a regular Sudoku until it is solved.  Good luck!

Gareth

I’m very pleased to announce that as of 24 hours ago Sudoku Xtra issue 2 is available for download or ordering in printed form.

It contains a staggering 121 puzzles, with only just a few of each type so there is a huge range of variety. At just £2.95/$4.95 it really is great value, but if you’re still not sure take a look at the sample part of issue 1 still available on the Sudoku Xtra site.

New puzzles for this issue include some crazy Sudoku variants, such as Samurai Killer Calcudoku Inequality, and a whole load of novel community-supplied puzzles, including Puzzle L and Knight’s Tour.

With so many different puzzles you’re sure to find not just one but lots of puzzles you’ll enjoy, so check out Sudoku Xtra today!

Futoshiki 7×7 puzzle

Futoshiki 6×6 puzzle

It’s been a little quiet here the past week or so due to circumstances beyond my control, but in preparation for the launch of Sudoku Xtra issue 2 tomorrow I thought it would be fun to post a couple of left-over puzzles here.  These are nothing particularly unusual, I’m afraid – just some regular Futoshiki puzzles, in fact, but I don’t think I’ve posted any of these to this blog before so it was probably about time I did!

The rules of the puzzle are really simple – just place 1 to 6 or 1 to 7 into each row and column, whilst obeying the inequality signs (this means that the arrows should point at the lower number of each adjacent pair, where shown).

I’ve mixed up the already varied puzzle sizes a bit more in Sudoku Xtra issue 2, so several of the puzzle types that were all 9×9 in issue 1 are now at a range of sizes (mostly 6×6, 8×8, 9×9, 10×10).  I’ve also tried to make sure the Skyscraper puzzles aren’t quite so tricky as last time round!  In fact I’ve tried to make sure there’s a slightly wider range of difficulties on many of the types.  This is something I’ll refine further over future issues, as I continue to find out what people think of the various puzzles.

I’m still putting the finishing touches to the issue, so I’d better get back to that now. Enjoy the Futoshiki!

Inequality Calcudoku puzzle

Here’s a fun little puzzle – a Calcudoku Inequality puzzle.

Just place 1 to 6 into each row and column whilst obeying the bold-lined cages’ operator totals. These give the result of applying the stated operator between all numbers in that region, so for example the result of adding together all the squares in a ‘24+’ region must be 24. Similarly the squares in the 1728x region must all multiply to that total. Unlike in Killer Sudoku, you can repeat a value within a cage (but you must still obey the constraint to not repeat a number in a row or column).

There are also some inequalities marked. These show that the value of one square is lower than the value of a square next to it. The arrow always points to the smaller number.

Good luck!