Sudoku Snake 9×9 1 puzzle

Each of the shaded snakes consists of only ‘consecutive’ cells along its length, which means that any two cells joined by a snake must have values with a difference of 1, such as 2&3 or 7&8.  So for example the 4-square-long snake at the top-left might have 2323 along its length, or any valid fit such as that.

In addition follow usual sudoku rules. Also note that only the cells joined by the snakes have any special relationship – any other pair of cells may or may not be consecutive (unlike in regular consecutive sudoku).

Non-consecutive Sudoku puzzle

I thought I’d start off with Non-Consecutive Sudoku.  This is a minor variant on Consecutive Sudoku, where all the rules of standard Sudoku apply but there is one additional constraint:

• Neighbouring squares are not consecutive.  This means there is never a difference of ‘1′ between two edge-adjacent squares (i.e. touching, not including diagonally).

For example, if a square contains ‘3′ then any neighbouring square cannot contain either ‘2′ or ‘4′.

Good luck!

Consecutive Skyscraper puzzle

It’s been a while since I posted a new puzzle here, what with all the excitement about Sudoku Xtra magazine, so I thought I had better do something about that right now!  So to that end, here’s something a little bit unusual – a Consecutive Skyscraper puzzle.

Now Consecutive Skyscraper may sound like a brief description of downtown Manhattan, but in fact it’s a puzzle with pretty simple rules:

• Place 1 to 8 in each row and column
• Obey the Skyscraper constraints: each number outside the grid reveals the number of ‘visible’ digits looking along that row/column, where higher digits obscure all lower ones
• White bars between squares reveal all consecutive squares – those where the difference is one (such as 1&2, 2&3, etc).  Squares without white bars between are not consecutive

If that isn’t detailed enough for you, try clicking the relevant links on the right, or here’s what I wrote back in April about Skyscraper puzzles:

In a Skyscraper puzzle you place numbers in a grid whilst obeying ‘building height’ constraints around the edge. These building height constraints specify the number of notional buildings you could see whilst standing at the edge of the puzzle and looking in, whereby a taller building completely hides the view of any shorter building.  The idea is that a digit ‘1′ in the grid is a building 1 storey high; a digit ‘2′ in the grid is a building 2 storeys high, and so on.

If you had a very simple 3×3 Skyscraper puzzle, here’s the potential solutions to each of the possible clues:

• 1: can be either 3 2 1 or 3 1 2, with the ‘3′ hiding both the other digits
• 2: can be 1 3 2 or 2 3 1 or 2 1 3.
• 3: can only be 1 2 3 because this is the only way to see all of the buildings.

Good luck!

Wrap-around Consecutive Samurai Star puzzle

I seem to be posting more infrequently than I intend, so I thought I’d compensate with a puzzle that would take somewhat longer to complete!  Here, then, is a wrap-around consecutive samurai star.  All squares with consecutive values (a difference of 1) are marked with white bars, including those at opposite ends of rows and columns – wherever there isn’t a bar, the values are not consecutive.

The Sudoku logic takes a few twists here and there – in fact at one point near the end you will need to spot a particularly nasty hidden set in one region.

To solve the puzzle place 1 to 9 into each row, column and 3×3 box of each of the underlying 5 Sudoku grids (including the one in the centre).  You’re only given 4 givens to get going, but with the consecutive information that’s all you need to find a unique solution.

Good luck!

Consecutive 12×12 Sudoku puzzle

After a bit of a break to meet a major book deadline – the non-consecutive part of the title of this posting – I’m back with what seems to be one of the most popular types of puzzle, a Consecutive Sudoku.  I wanted something a little bit different, though, so this is a Consecutive Sudoku 12×12.  I personally always find Sudoku 12×12 pretty similar to regular 9×9 Sudoku to solve, unlike something like 16×16 which personally I’d never really bother with (apologies to anyone who loves them!).

In order to make the consecutive nature of the 12 possible values obvious, I’ve used one- and two-digit numbers rather than digits and letters.  So the rules are simple: place 1 to 12 into each row, column and 4×3 box whilst obeying the white consecutive markers.  Wherever there is a white consecutive marker between two squares then the difference of value in those two squares is 1; and conversely whereever there is no marker the difference is always greater than 1.

So sorry for the break – hopefully ‘normal’ service will now be resumed!

And good luck with the puzzle!

Consecutive Skyscraper 8×8 puzzle

Here’s a combination I haven’t posted before – a standard skyscraper puzzle with the addition of consecutive markers between adjacent squares.  This allows the creation of an 8×8 puzzle without needing to also add Sudoku boxes.

The rules are as follows:

• Place 1-8 in each row and column
• Numbers outside the grid reveal the number of ‘visible’ numbers looking along that row/column, where higher numbers obscure lower ones
• White bars between squares reveal all consecutive squares – those where the difference is one

Good luck!

Wrap-around Consecutive 3-grid 6×6 Samurai Skyscraper puzzle

Another mouthful of a puzzle name, but in essence simply a development of the previous puzzle I posted.  This time we still have the wrap-around consecutive-ness, but I’ve extended it to a samurai puzzle and added in skyscraper clues.  To keep it reasonable, I’ve reduced the underylying Sudoku size to 6×6, however!

What’s particularly fun about the wrap-around markers is that they warp from one side of the puzzle to the same row/column on the opposite side – for the centre two columns this means that they constrain the values of two numbers 10 squares apart.

So the full rules are:

• Place 1 to 6 into each row, column and 2×3 bold-lined box of each of the three underlying 6×6 grids
• White bars show that adjacent cells are consecutive – i.e. 1&2, 2&3, 3&4, 4&5 or 5&6; those squares without a white bar between are non-consecutive
• White bars are shown where appropriate even on the edges of the grid –  they indicate how the cell relates to the square at the far end of this row/column of numbers.  Remember that the lack of such a white bar means that these wrap-around squares are non-consecutive.
• Skyscraper clues reveal how many numbers can be ’seen’ from that clue number counting in along the adjacent row/column, where higher numbers obscure all lower numbers (see previous puzzles for more detailed instructions)

Just to clarify, if adjacent numbers are equal (which is possible if they’re at far sides of the grid from one another) then these count as non-consecutive.

Good luck!

Consecutive Wrap-around Fiendish Sudoku puzzle

Here’s a slight twist on Consecutive Sudoku – I’ve included ‘wrap-around’ consecutive indication, where rows that start and end in consecutive digits have a white bar at the start and end of the row to show this, and similarly for columns. If they’re non-consecutive then there is no white bar.  Similarly between all other squares: a white bar indiciates that two squares are consecutive, and no white bar means that they are non-consecutive.

‘Consecutive’ means that the difference between the numbers is ‘1′, i.e. they are 1&2, 2&3, 3&4, 4&5, 5&6, 6&7, 7&8 or 8&9.   Other than this it’s a regular Sudoku – place 1 to 9 into each row, column and bold-lined 3×3 box.

This is also a difficult Sudoku, so if you can solve it under 20 minutes that would definitely be good going.   Don’t forget about the non-consecutiveness – this is very important to reach the solution, and don’t forget about the wrap-around!

Good luck!

Samurai Consecutive Sudoku

I thought it would be a nice idea to create a large Consecutive Sudoku for the weekend!  And so here one is: a 5-grid Samurai Consecutive Sudoku.  As you can see, there are very few givens to start with, so it will hopefully be at least a bit of a challenge!  (It shouldn’t be as tricky as the Skyscraper version, at least once you get going!).

I’ve also decided to make Consecutive Sudoku the ‘puzzle of the month’ (”Masterclass”) puzzle in Sudoku Pro issue 45, which should be out in just under 2 months I think.  Hopefully I’ll also make a book of them available online soon(ish!).

The rules for this Consecutive Samurai are simple: place 1 to 9 into each row, column and bold-lined 3×3 box of each of the 5 Sudoku grids, whilst also obeying the consecutive constraints – numbers with a white bar between are consecutive, whilst those without a white bar between are not consecutive.  ”Consecutive” means that the difference between the values in the two squares is exactly 1: i.e. 1&2, 2&3, 3&4, 4&5, 5&6, 6&7, 7&8 or 8&9.

Good luck!

Samurai Star Consecutive puzzle

If the smaller consecutive puzzles weren’t enough of a challenge then this one should be!  There are five overlaid 9×9 grids (including a ‘hidden’ one in the middle) which each need to have 1 to 9 placed into every row, column and bold-lined 3×3 box.  On top of this you must obey the consecutive constraints – numbers with a white bar between are consecutive (12, 23, 34, 45, 56, 67, 78 or 89) and those without a bar between are not consecutive.

As you can see, the combination of tightly-overlaid grids and the consecutive marks means that very few givens are needed!  Remember that none of these puzzles need ‘complex’ solving logic (you don’t need hidden or naked sets, X-wings or any other even more exotic strategy).

Good luck!

PS If there are any particular Sudoku or Samurai variants you’d like to see, please let me know and I’ll see what I can do!

Skyscraper Consecutive Sudoku puzzle

Many of the best Sudoku variations can be combined with other variations in order to produce yet more types of puzzle.  One variety I’ve personally never seen is to combine Skyscraper and Consecutive Sudoku together, so I thought I’d try it out today!

Skyscraper puzzles themselves are pleasant little puzzles where you must place 1 to 7 (or smaller) into each row and column of a grid whilst obeying ‘building height’ constraints around the edge.  There’s an example 7×7 puzzle on this page over at puzzlemix.  These building height constraints specify the number of notional buildings you could see whilst standing at the edge of the puzzle and looking in, whereby a taller building completely hides the view of any shorter building.  The idea is that a digit ‘1′ in the grid is a building 1 storey high; a digit ‘2′ in the grid is a building 2 storeys high, and so on. 

If you have a very simple 3×3 Skyscraper puzzle, here’s the potential solutions to each of the possible clues:

• 1: can be either 3 2 1 or 3 1 2, with the ‘3′ hiding both the other digits
• 2: can be 1 3 2 or 2 3 1 or 2 1 3.
• 3: can only be 1 2 3 because this is the only way to see all of the buildings.

I think that the maximum size of Skyscraper puzzle you can make without using any pre-solved numbers (givens) is 7×7, but by combining it with additional Sudoku constraints (i.e. the 3×3 boxes, and some given numbers in the puzzle already) you can make much larger puzzles.

Example Consecutive Sudoku Skyscraper solution

So what we have here is a Skyscraper Sudoku – you must place 1 to 9 into each of the rows, columns and bold-lined 3×3 boxes whilst obeying the Skyscraper building height constraints around the edge of the puzzle.  And then just to add an extra twist further to the puzzle, I’ve also included consecutive/non-consecutive constraints as in the previous days’ puzzles – click here for full instructions for these, but the basic idea is that a white bar separates two squares that have consecutive values (i.e. the mathematical difference is 1, so specifically 1&2, 2&3, 3&4, 4&5, 5&6, 6&7, 7&8 or 8&9) and if there’s no white bar then the difference is greater than 1 (i.e. they’re not consecutive).

I’ve attached an example 4×4 puzzle so you can be sure you understand how the Skyscraper (and consecutive) constraints work with this type of puzzle.

Good luck!

Consecutive 2-grid Samurai Sudoku

Well I promised a larger Consecutive Sudoku puzzle yesterday, and here one certainly is!  It’s a 2-grid Consecutive Samurai Sudoku puzzle and the rules are essentially exactly the same as for yesterday’s puzzle except applied to a much larger grid.

The aim is to fit 1 to 9 into each of the rows, columns and 3×3 boxes of both of the two overlapping 9×9 puzzle grids, whilst obeying the consecutive constraints.  In quick summary (read my full description yesterday), squares separated by a white bar contain values that are ‘consecutive’ – have a difference in value of exactly 1 – and those squares without a white bar between them are not consecutive – they have a difference in value greater than 1.

This puzzle is much trickier than my 6×6 example.  It will probably take you half an hour or more to solve, of which by far the hardest part is working out how to start.  Once you get going (which doesn’t require writing in ridiculous numbers of pencilmarks, I promise) it should keep flowing pretty smoothly.

If you need a hint then, the short version is this:

• You only have a few given numbers, so focus on areas around these – you don’t really need to worry about entirely empty parts of the grid far away from the givens to get going.
• Remember to solve both grids simultaneously and pay attention to the non-consecutive squares too!
• Focus on the centre 3×3 box – the information from both grids will help you make progress on it (and then from there you can actually consider both grids mostly independently)

A more detailed hint (but only a hint – not full instructions for getting going!) is this: after filling a few easy numbers around the ‘9′ in the bottom-right grid, the secret is to consider where a ‘9′ can go in the very centre box.  Part of this deduction is remembering (and this is critical!) not just to pay attention to the consecutive squares but also the non-consecutive ones!  Noting that the number directly below the ‘8′ in the centre 3×3 box of the top-left grid cannot possibly be a 7 or a 9 (and therefore the number to the right of that cannot be an 8, and the one to the right of that can’t be a 9) is a critical part of this process, along with a few deductions based around possible placements of 9s in the left three columns of the bottom-right 9×9 grid.

Good luck!  (Once you get going this is a really fun puzzle!)

Standard Sudoku 6×6 puzzle

Consecutive Sudoku 6×6 puzzle

A Sudoku variant that I have always wanted to create, but somehow have just not quite ever got round to actually doing, is Consecutive Sudoku.

In Consecutive Sudoku, hollow bars between squares indicate that those two squares contain consecutive values – that is, each square is either one higher or one lower in value than the other.  So if a square contains ‘3′ and there is a hollow bar between it and another square then that other square must contain either ‘2′ or ‘4′ – this is the consecutive constraint.

What makes it even more interesting is that the converse also applies – if there is not a hollow bar then the neighbouring squares are not consecutive.  Therefore if a square contains ‘3′ then any neighbouring square without a hollow bar between them cannot contain either ‘2′ or ‘4′.

It might sound slightly complicated, but in fact the real beauty of this Sudoku variant is that it is actually beautifully simple when you come down to actually trying it.  And what’s more, puzzles turn out to be considerably easier than you might imagine – the consecutive constraint is simple enough to trace and follow that it really helps you solve the puzzle, rather than being a complex relationship that just adds to the solving difficulty!

You also get the chance to use some new logic – it’s a very little bit like Futoshiki or Inequality Sudoku, but with (to me) a cleaner, more elegant solving path.

I’ve made an example puzzle.  It’s 6×6 because it makes it easier to follow the rules if you’re new to the type – I’ll post some much larger versions soon, I promise!

Attached to this post are two puzzles, each leading to the same solution.  The first is a (rather attractive circular) regular 6×6 Sudoku, which will give you the solution pretty easily if you need some help.  The other is the consecutive version of the puzzle.  As you can see, it has far less givens – just 4!  But this is all that is needed.  It shouldn’t take more than a few minutes to solve, I promise.

Standard Sudoku rules apply – place 1 to 6 into each row, column and 2×3 bold-lined box.

Good luck!

PS Just in case it isn’t obvious, when you click on the puzzle graphics they will open and load into a PDF viewer such as Adobe Acrobat (if you don’t have it click here to get it).

PPS And if you want to comment – e.g. say if you like this sort of puzzle and want to see more, or comment on how long it took you to solve it/how easy it was, then click on ‘No comments’  at the top of this post, or just click on the post title itself to open it in a new window with comments and comment box included.