## Skyscraper variants

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Skyscraper variants

I was trying to create some interesting skyscraper variants over the past week. Some of them were quite interesting to make. What I offer here are some of my better creations.

Regular skyscraper: Fill the grid with the digits 1 to 9. The digits represent the height of the Skyscraper in each cell. Each row, column and 3x3-box will have exactly one of each digit. The clues along the egdes tell you how many Skyscrapers you can see from that vantage point.

http://www.sachsentext.de/en/index.htm (Pyrrhon's website?) contains 2 examples of these. I think that the difficulty of my skyscrpaer sudoku is inbetween that of the two posted on Pyrrhon's site. It shouldn't be too difficult.

Skyscraper sudoku X: as regular skyscraper, except with additional regions on the main diagonals. Once again, should not pose too much of a challenge.

The least number of givens possible on a regular skyscraper is 6. (placing 9 6 _ | 8 5 _ | 7 4 _ along the top). The least number of possible givens on a skyscraper X, on the other hand, should be larger, even though there are more constaints. If somebody were able to calculate that, that would be great.

Killer skyscraper. Another predictable variant, but one with lots of potential. This one's a medium pearl, and should be fairly difficult.

Diagonal Skyscraper: This time, the digits on the outside of the sudoku represent the sum of the number of skyscrapers that you can see along the two (or one) diagonals from that vantage point. If two skyscrapers of the same height are next to each other, you can only see the first one. This one is a good difficulty and an interesting twist. I would highly recommend it.

Even/Odd skyscraper: Shaded regions represent even numbers, unshaded regions represent odd numbers. This is another interesting puzzle, and once again, I recommend it.

Lastly, here's a difference skyscraper sudoku. The numbers represent the positive difference between the two adjacent cells.

Enjoy!

~Squirrel
Last edited by Squirrel on Fri Nov 24, 2006 6:12 pm, edited 1 time in total.
Squirrel

Posts: 11
Joined: 25 September 2006

Thanky ou for your variants. I will try them. Only a little remark: The variant you call diagonal skyscraper you can also find at Hexapuzzle.hu. It is called there sudoku blocks.

Pyrrhon
Pyrrhon

Posts: 240
Joined: 26 April 2006

Has somebody solved the difference puzzle? I'm always coming to contradictions in my walk.

Uwe
Pyrrhon

Posts: 240
Joined: 26 April 2006

I like to add some other skyscraper variant puzzles:

Argyle Skyscraper Sudoku

In the marked diagonals no digit can appear more then once.

10 Sum Skyscraper Sudoku

Taking 180-degree rotational symmetry, the sum of mirrored skyscrapers must be 10.

Greater/Less Skyscraper Sudoku

Heights of skyscrapers must be placed according to greater (>) and less (<) signs.

Navigator Skyscraper Sudoku

The arrows show the location of the same number in the previous or next column or row. So for example, the arrow next to the 2 in the first column means that the 2 in the second column is in row 6 - 9.

The red points in the near of crosses where four cells meet each other show that the cell with the red point is greater then the three other ones.

Difference Skyscraper Sudoku (2nd variant)

The numbers between two cells give the difference of the heights.

Even/Odd Skyscraper Sudoku (2nd variant)

Yellow cells must contain odd digits, green cells must contain even digits.

Jigsaw Skyscraper Sudoku

Each row, column and cells of the same color will have exactly one of each digit.

Arrow Skyscraper Sudoku

The digit in a circle is the sum of the digits which are marked with its arrow.

Nonconsecutive Skyscraper Sudoku

There are no neighbouring houses with consecutive skyscraper heights.

Last edited by Pyrrhon on Sun Nov 05, 2006 4:12 am, edited 1 time in total.
Pyrrhon

Posts: 240
Joined: 26 April 2006

Uwe, you keep silently adding puzzles to this thread, I think not many have noticed the changes...

My suggestion is to open a new reply post each time you post a batch of puzzles, or at least add a line of "time of update" at the end of the original post...

It's just a mild suggestion so please don't feel compelled or anything...
udosuk

Posts: 2698
Joined: 17 July 2005

You are right, but it was still the last post in this thread. I add now the nonconsecutive skyscraper and stopp the skyscraper production. I only think about a Skyscraper Smash (combination of all these skyscraper combinations). If you are interested you can find two more even/odd skyscrapers (slightly different variants) and another skyscraper sudoku x at my page.

Uwe
Pyrrhon

Posts: 240
Joined: 26 April 2006

Creasing Skyscraper Sudoku

Numbers going along grey lines must be in increasing or decreasing order from one end to the other.

Pyrrhon

Posts: 240
Joined: 26 April 2006

With respect to better overview, I've made no skyscraper smash sudoku, but a combination of some skyscraper variants.

Combined Skyscraper Sudoku

Its an skyscraper with the following additions:

Box 1 - Even/Odd Sudoku: Yellow cells must contain odd digits, green cells must contain even digits.
Box 2 - Min Max Quad Sudoku: The red points in the near of crosses where four cells meet each other show that the cell with the red points is greater then the three other ones. The blue rings in the near of crosses where four cells meet each other show that the cell with the blue ring is smaller then the three other ones.
Box 3 - Arrow Sudoku: The digit in the circle is the sum of the digits which are marked with its arrow.
Box 4 - Difference Sudoku: The numbers between two cells give the difference of the digits.
Box 5 - Navigator Sudoku: The arrows show the location of the same number in the previous or next column or row. So for example, the arrow in fifth column means that the same digit is in the sixth column in row 6 - 9.
Box 6 - Greater/Less Sudoku: The inequality between each pair of digits must stand correct.
Box 7 - Ratio Sudoku: The numbers between two cells give the ratio of the digits. For example 2/3 can stand for the following combinations of numbers in the adjazent cells: 2 - 3, 4 - 6, 6 - 9 and vice versa.
Box 8 - Killer Sudoku: Digits in a sub-region add up to the specified number.
Box 9 - Creasing Sudoku: Numbers going along grey lines must be in increasing or decreasing order from one end to the other.
There is only one solution. You can find it by logic.

Pyrrhon

Posts: 240
Joined: 26 April 2006

Pyrrhon wrote:Has somebody solved the difference puzzle? I'm always coming to contradictions in my walk.

Uwe

I've tried the difference puzzle also, and either I'm missing something or there's an inconsistency.

Cells R6C4 and R6C5 have to be (1,9). And R5C4 and R5C5 have to be (4,6). But the difference between R5C4 and R5C5 has to be 3, but it's actually 2.

Help!!
Mel-o-rama

Posts: 19
Joined: 02 February 2006

Oops. 2 posts, 2 mistakes, I'm on a bad roll here. That actually is a 2 in the middle nonet, sorry about the confusion. I'll also double check my others to make sure they're all correct as well.

Sorry,

~Squirrel
Squirrel

Posts: 11
Joined: 25 September 2006

Okay, just let us know when you've double-checked the differences. It looks like an enjoyable puzzle. There appears to be another inconsistency in Nonet 4 where R5C1 must be (4,6), contradicting R5C4 and R5C5 being (4,6).
Mel-o-rama

Posts: 19
Joined: 02 February 2006

It should be fine, all the numbers were correct. I'm not sure where you're going wrong in the middle column, maybe you corrected the wrong number in the previous correction, I've updated the image on the origonal post, and all the numbers are correct. Here's what you should be getting for the those two nonets:

Code: Select all
` |37 28 19|28 37 46||46 5  19|46 37 28||37 28 46|19 19 5 |`

Sorry for any confusion,

~Squirrel
Squirrel

Posts: 11
Joined: 25 September 2006

Okay, now I can solve it, and get

415287693
876953241
932614578
729836415
651472389
384195762
293761854
147528936
568349127

using naked and hidden single, naked pair, obsolete values by the difference property and the difference between column 6 and 7 looking from the bottom to the top.
Pyrrhon

Posts: 240
Joined: 26 April 2006

Pandigital Skyscraper Sudoku

Additional the rows form 9 correct arithmetic expressions reading from left to right.

Disallowed Skyscraper Sudoku

The second is the sudokification of a skyscraper variant from that I found some puzzles made by Inaba Naoki at janko.at

If a clue is cancelled with a red cross then you can't see this number of skyscrapers.

Pyrrhon

Posts: 240
Joined: 26 April 2006

Squirrel wrote:It should be fine, all the numbers were correct. I'm not sure where you're going wrong in the middle column, maybe you corrected the wrong number in the previous correction, I've updated the image on the origonal post, and all the numbers are correct. Here's what you should be getting for the those two nonets:

Code: Select all
` |37 28 19|28 37 46||46 5  19|46 37 28||37 28 46|19 19 5 |`

Sorry for any confusion,

~Squirrel

Thanks - I'm going to give it another go over the holidays. (I can't seem to recreate my problem - oh well.)
Mel-o-rama

Posts: 19
Joined: 02 February 2006

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