Sum-Skyscraper 5×5 puzzle

This is a Sum Skyscraper. Place the digits 1 to 5 once each into every row and column in the grid. Numbers outside the grid provide the total (i.e. sum) of ‘visible’ grid digits along that row or column, if you imagine each digit as a building of that many storeys. Taller buildings always obscure shorter ones. So, for example, a clue for 21354 from the top of such a column would be 10, since the 2, 3 and 5 are visible (the 1 and 4 are obscured by the 2 and 5 respectively), and 2+3+5 = 10.

Sum Skyscraper 6×6 puzzle

Sum Skyscraper 5×5 puzzle

Sum Skyscraper puzzles are very similar to Skyscraper puzzles, so no number can repeat in any row or column and external ’skyscraper’ clues reveal information about the numbers in the main grid. In 5×5 puzzles place 1-5, and in 6×6 puzzles place 1-6.

Each number in the completed grid represents a building of that many storeys, and place the buildings in such a way that each given number outside the grid represents the sum of the number of buildings that can be seen from that point, looking only at that number’s row or column. A building with a higher value always obscures a building with a lower value, while a building with a lower value never obscures a building with a higher value. So the clue ‘6′ in a 5×5 puzzle would indicate that the buildings ‘1′ and ‘5′ can be seen (’5′ is always visible in 5×5 puzzles), so the solution to a row might be 15234.

Skyscraper 5×5 2 puzzle

Skyscraper 5×5 1 puzzle

Skyscraper puzzles combine the no-repeat row and column constraints of sudoku with novel additional clues. In these 5×5 puzzles, place the numbers 1-5 once each into every row and column. Each number in the completed grid represents a building of that many storeys.

Place the buildings in such a way that each given number outside the grid represents the number of buildings that can be seen from that point, looking only at that number’s row or column. A building with a higher value always obscures a building with a lower value, while a building with a lower value never obscures a building with a higher value.

I’ve just added Skyscraper puzzle support to Puzzlemix. Hop on over if you’d like to try playing Skyscraper puzzles online!

This means that there are now 16 different types of puzzle on the site, plus a variety of sizes for each of those puzzle types.

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!

Skyscraper Sudoku 8×8 puzzle

Continuing my series of 8×8 Skyscrapers and variants, here’s an 8×8 Sudoku with Skyscraper clues around the edge.

The rules are simple:

• Place 1 to 8 in each row, column and 4×2 box
• Obey the Skyscraper constraints: each number outside the grid reveals the number of ‘visible’ digits looking along that row/column, where higher digits obscure lower ones

Good luck!

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!

Skyscraper Shuriken Samurai Sudoku puzzle

I’m glad yesterday’s Shuriken Samurai went down well, so today I’ve upgraded it to a Skyscraper puzzle (following Christine’s request for more Skyscrapers!).  This is, I think it’s fair to say, quite a bit harder than the basic Samurai yesterday was – but then any puzzle with a title this hard to say quickly really shouldn’t be able to be solved quickly either…

The rules are the same as yesterday (place 1-6 into each row, column and 2×3 box of the 13 underlying 6×6 Sudoku grids) but with the addition of Skyscraper constraints: place numbers so that the given number of digits can be ’seen’ from each external Skyscraper clue outside the grid.  From the vantage point of each Skyscraper clue look along the adjacent row/column – with higher numbers obscuring all lower numbers (or those of the same value), the clue tells you how many numbers are visible.  Check back to older puzzles I’ve posted for more detailed help.

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!

Skyscraper Sudoku puzzle

It occurs to me that I didn’t get round to posting any ’straightforward’ Skyscraper Sudoku puzzles previously, so I thought I’d rectify that today.  Attached is a regular 9×9 Sudoku with the addition of Skyscraper clues around the edge, and no other twists!

For the Skyscraper clues the numbers around the edge represent the number of digits visible from that point looking in along the row/column, where higher digits obscure all lower digits.  So for example the solution to the clue ‘9′ would have to be 123456789, otherwise you couldn’t see all 9 digits; if the clue is ‘1′ then the first digit must be a 9, hiding all of the other digits.  However the solution to the clue ‘8′ might be 134567829, where the ‘2′ is “hidden” behind the higher digits, or one of several other possibilities.  For more examples and more detailed instructions click back to some of my older puzzle postings.

On a completely different topic, if you’ve had any trouble viewing the most recent few puzzles then I apologise – it turns out that some of them wouldn’t open in older versions of Adobe Acrobat Reader (version 7 wouldn’t open them, at any rate – the current version is 9.1).  I changed the way I make PDFs a week ago, but I hope I’ve now fixed what I think was causing the problem!  If today’s puzzle won’t open for you I’d be incredibly grateful if you could post a comment and tell me what PDF viewer you’re using and what error message you get!

Good luck with today’s puzzle!

Skyscraper 7×7 puzzle

Skyscraper 5×5 puzzle

It occurs to me that I haven’t yet posted a regular, vanilla Skyscraper puzzle, so I decided that today was the day to rectify that!  The 5×5 puzzle attached is pretty easy – it can be solved in under a minute if you’re on your toes!  The 7×7 is nowhere near as hard as many of the puzzles I’ve posted recently, but it will certainly take longer than that.

The rules are simple: place 1 to 5 (or 1 to 7) into each row and column whilst obeying the skyscraper constraints.  In Skyscraper puzzles each number in the completed grid represents a building of that many storeys, so the aim is to place the buildings in such a way that each given number outside the grid represents the number of buildings that can be seen from that point, looking along the adjacent row/column.  A building with a higher value always obscures a building with a lower value, and a building with a lower value never obscures a building with a higher value.  (Click back and look at some of my older posts for more details and examples)

Also, I want to say thanks very much for all of the fantastic comments that have been posted in response to my other puzzles – I’ve read them all and taken note and am working on suitable puzzles to follow up!

Samurai 5-grid Skyscraper puzzle

I thought I’d try one more Skyscraper Samurai Sudoku puzzle – this time a 5-grid variety, or what I think of as the ‘traditional’ Samurai Sudoku format (some people also call this Gattai-5, but I’ve not seen that in print anywhere).

The aim is to place 1 to 9 into each row, column and 3×3 bold-lined box of each of the 5 9×9 Sudoku grids, whilst also obeying the Skyscraper constraints.  These tell you the number of digits that can be ’seen’ from the edge of the grid looking in along the adjacent row/column, where higher numbers obscure lower ones.  Take a look at a couple of last week’s puzzles if you need more detailed instructions for this constraint.

As has been pointed out in the comments elsewhere, it doesn’t matter whether you consider that the Skyscraper clues apply to the nearest 9×9 grid or to the entire width/height of the row/column they attach to – once the first ‘9′ is reached then there are no higher numbers, and that’s guaranteed to happen within the first 9 squares.

I think this is probably about as large as you want to go with a relatively complex constraint such as Skyscraper, which is why I’ve included quite a few given numbers too – including some which clearly aren’t needed to give the puzzle a unique solution.  (But please tell me if I’m wrong about this being big enough – I could always make a much larger one still just to prove that it’s possible!)

This week I plan to try out some other types of consecutive Sudoku variant – there are a couple of moderately-well-known types where you specify certain relationships between adjacent squares, such as ‘x2′ (where one number is twice the adjacent one – a bit like a slightly less-constrained version of consecutive sudoku!).  If you have any ideas for other variants,  feel free to let me know – I might try them out!

Good luck!

Skyscraper Jigsaw Samurai Sudoku puzzle

I’m pretty confident that you won’t have come across one of these puzzles before – I certainly haven’t!  It’s a Samurai Skyscraper Sudoku puzzle with Jigsaw regions instead of regular 3×3 boxes.

The aim is to place 1 to 9 into each row and column of each of the two overlapping 9×9 grids, and also place 1 to 9 into each of the bold-lined jigsaw pieces.  On top of that, you must also obey the Skyscraper constraints, which are the numbers outside the main puzzle grid.  They specify the number of digits you can ’see’ from each point, where higher digits obscure lower digits (so a 7 obscures 1 to 6, and a 9 obscures all other digits, for example) – see yesterday’s post for a slightly longer explanation of how these constraints work.

Good luck!

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!