Consecutive Sudoku
Consecutive Skyscraper
Nov 24th
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
Jul 6th
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!
(Non-consecutive) Consecutive Sudoku 12×12
Jun 30th
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
Jun 17th
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
May 18th
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 Sudoku
May 16th
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!
Consecutive 5-grid Samurai Sudoku
Apr 24th
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!
Consecutive Samurai Star
Apr 17th
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
Apr 15th
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 Samurai Sudoku
Apr 14th
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!)
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