## How to even get started on this skyscraper sudoku?

For fans of Killer Sudoku, Samurai Sudoku and other variants

### How to even get started on this skyscraper sudoku?

Hi everyone,

I've found this 7x7 skyscraper sudoku and i don't know how to even get started on it!
Code: Select all
`         2                   5   +---+---+---+---+---+---+---+ 5 |   |   |   |   |   |   |   |   +---+---+---+---+---+---+---+   |   |   |   |   |   |   |   |   +---+---+---+---+---+---+---+   |   |   |   |   |   |   |   |   +---+---+---+---+---+---+---+ 3 |   |   |   |   |   |   |   | 4   +---+---+---+---+---+---+---+ 2 |   |   |   |   |   |   |   |   +---+---+---+---+---+---+---+ 2 |   |   |   |   |   |   |   |   +---+---+---+---+---+---+---+ 3 |   |   |   |   |   |   |   |   +---+---+---+---+---+---+---+     5       4       5`

Usually with no givens, i start looking at possibilities for the highest skyscraper.
So if i put in 7s in all possible places it looks like this:
Code: Select all
`         2                   5   +---+---+---+---+---+---+---+ 5 |   |   |   |   | 7 | 7 |   |   +---+---+---+---+---+---+---+   | 7 | 7 | 7 | 7 | 7 | 7 |   |   +---+---+---+---+---+---+---+   | 7 | 7 | 7 | 7 | 7 | 7 |   |   +---+---+---+---+---+---+---+ 3 |   |   | 7 | 7 |   |   |   | 4   +---+---+---+---+---+---+---+ 2 |   | 7 |   | 7 |   | 7 | 7 |   +---+---+---+---+---+---+---+ 2 |   | 7 |   | 7 |   | 7 | 7 |   +---+---+---+---+---+---+---+ 3 |   |   |   | 7 |   | 7 | 7 |   +---+---+---+---+---+---+---+     5       4       5`

But i totally fail how i could now eliminate more options. Looking at the 6s surely won't help as there would be way more options.
So what am i missing here?

Can someone help me get started? Or point me to a page with advanced skyscraper sudoku solving techniques?

Much thanks,
.dom
domz

Posts: 11
Joined: 16 September 2017

### Re: How to even get started on this skyscraper sudoku?

Hi domz

I have an idea. If r5c7=7, from the outside of r5, we know that r5c1 must contain 6. And then there`s a contradiction in c1(because the outside in c1 is 5). So r5c7 can`t contain 7. For the same reason, r6c7 can`t contain 7. So r7c7 must contain 7.

Hope it helps you.

Scarlet
Scarlet

Posts: 9
Joined: 06 June 2019

### Re: How to even get started on this skyscraper sudoku?

Because of the outside number of c135, digit 6 cannot contain in r7c135 in r7. Because the outside number of c1 and c5 is 5, then r7c1 and r7c5 = 123. If r7c4 = 6, then r7c1 = 3, r7c2 = 2, r7c1 = 1 (according to the outside number of r7). Then r7c5 has no solution. So r7c4 is not 6. If r7c6 = 7, then 5 must be at r7c1, so c1 has no solution. So 6 in r7 can only be in r7c2.

(Maybe I didn't make it clear. Let's see what other people think)
Scarlet

Posts: 9
Joined: 06 June 2019

### Re: How to even get started on this skyscraper sudoku?

SudoKai

Posts: 45
Joined: 07 June 2014
Location: South-Africa

### Re: How to even get started on this skyscraper sudoku?

Hey Scarlet,

Wow, that was tremendously helpful. Thank you very much!
Placing that first 7 and 6 really cut the knot for me. From there you can deduct more 7s and i finally could get started on tis puzzle

Cheers and keep on puzzling,
domz

PS: also thanks to SudoKai for the link, won't forget you
domz

Posts: 11
Joined: 16 September 2017

### Re: How to even get started on this skyscraper sudoku?

Hi domz

You are welcome. There is no denying that this puzzle is very difficult.

Just now, I used X-Wing and a lot of naked pair and naked triple to solve this problem. Maybe you can get a lot of useful information by repeatedly using the digit in the outside.

I hope to hear the good news for you to solve it

PS：We can also discuss this puzzle together

Scarlet
Scarlet

Posts: 9
Joined: 06 June 2019

### Re: How to even get started on this skyscraper sudoku?

Hello Scarlet,

Indeed, this is a very hard one. It may very well be beyond my capabilities

I'm not very experienced with skyscraper sudokus, but i really love digging into these logic riddles. Though i'm not the fastest one (as you may have noticed but i'm not giving up yet!

Also happy to discuss, although it sounds like you already solved it. So it's probably more you giving hints to me than a real discussion but i'd really appreciate it, as it looks i need some guidance there.

So after your initial tips i thought i got a lot of traction on 7s and 6s too and quickly reached this stage:
Code: Select all
`         2                   5   +---+---+---+---+---+---+---+ 5 |   |   |   | 6 | 7 |   |   |   +---+---+---+---+---+---+---+   | 7 |   | 6 |   |   |   |   |   +---+---+---+---+---+---+---+   | 6 | 7 |   |   |   |   | 4 |   +---+---+---+---+---+---+---+ 3 |   | 5 | 7 |   | 6 |   |   | 4   +---+---+---+---+---+---+---+ 2 | 5 |   |   |   |   | 7 | 6 |   +---+---+---+---+---+---+---+ 2 |   | 1 |   | 7 |   | 6 | 5 |   +---+---+---+---+---+---+---+ 3 |   | 6 |   |   |   |   | 7 |   +---+---+---+---+---+---+---+     5       4       5`

It's been a few days and just had another look now. While it looks like i didn't break any clues so far, i still believe this is not right.
Simply because i can't recall how i placed the 7s in row 5 and 6. There seem to be a lot more valid options and i think i missed something there.

So i gave it a clean start and guess what? being more careful i failed to make any progress
The only thing i spotted was: if r6c6=7 then r6c1=5 or 6 => this breaks the 2 clue for r6 so r6c6 is not 7

Looking like this now:
Code: Select all
`         2                   5   +---+---+---+---+---+---+---+ 5 |   |   |   |   | 7 | 7 |   |   +---+---+---+---+---+---+---+   | 7 | 7 | 7 | 7 | 7 | 7 |   |   +---+---+---+---+---+---+---+   | 7 | 7 | 7 | 7 | 7 | 7 |   |   +---+---+---+---+---+---+---+ 3 |   |   | 7 | 7 |   |   |   | 4   +---+---+---+---+---+---+---+ 2 |   | 7 |   | 7 |   | 7 |   |   +---+---+---+---+---+---+---+ 2 |   | 7 |   | 7 |   |   |   |   +---+---+---+---+---+---+---+ 3 |   | 6 |   |   |   |   | 7 |   +---+---+---+---+---+---+---+     5       4       5`

where 6 and 7 in row 7 are placed digits, all others are pencil marks - is there a better way to display this here?

I'm mainly looking at c1 and r7 currently trying to place some digits - i believe for c1 there's a 67 pair in r23 and for r7 there's a 45 pair in c46 and a 123 pair in c135
just not sure what to make of that yet

Any push or tip in the right direction is highly appreciated

Cheers,
.dom
domz

Posts: 11
Joined: 16 September 2017

### Re: How to even get started on this skyscraper sudoku?

I may not remember it very well

I think there are some complicated hints here.We look at r6, digit 7 can not place in r6c1357(because of the clues in outside). If r6c2=7, then because the outside clue in c2, we know that r1c2 must contain 5, but there are some contradictions in r1. If r6c6=7, then because te outside clue in r6, we can infer that digit must contain in r6c7 and digit 5 must contain in r6c1, but there are some contradictions in r1. So digit 7 in r6 must contain in r6c4.

Scarlet
Scarlet

Posts: 9
Joined: 06 June 2019

### Re: How to even get started on this skyscraper sudoku?

I think you can eliminate r6c2 = 7, which means you have r6c4 = 7.

If r6c2 was 7, then r1c2 would have to be 5, which it cannot be ...

[I see that Scarlet came to same conclusion at the same time! ]

Mathimagics
2017 Supporter

Posts: 1621
Joined: 27 May 2015
Location: Canberra

### Re: How to even get started on this skyscraper sudoku?

Yes! that's so obvious and gives me a 7 in r6c4, which i already had in my first try. so maybe i wasn't on the wrong track after all

Thanks to both of you!!
domz

Posts: 11
Joined: 16 September 2017

### Re: How to even get started on this skyscraper sudoku?

Hello again,

Just wanted to report back that i finally made it
Code: Select all
`         2                   5   +---+---+---+---+---+---+---+ 5 | 2 | 4 | 5 | 6 | 7 | 3 | 1 |   +---+---+---+---+---+---+---+   | 7 | 3 | 6 | 5 | 4 | 1 | 2 |   +---+---+---+---+---+---+---+   | 6 | 7 | 1 | 3 | 5 | 2 | 4 |   +---+---+---+---+---+---+---+ 3 | 1 | 5 | 7 | 2 | 6 | 4 | 3 | 4   +---+---+---+---+---+---+---+ 2 | 5 | 2 | 4 | 1 | 3 | 7 | 6 |   +---+---+---+---+---+---+---+ 2 | 4 | 1 | 3 | 7 | 2 | 6 | 5 |   +---+---+---+---+---+---+---+ 3 | 3 | 6 | 2 | 4 | 1 | 5 | 7 |   +---+---+---+---+---+---+---+     5       4       5`

It was not easy, but i enjoyed it very much and learned a lot along the way
Also thanks again for the help and tips provided - would have been stuck forever without!

On a related note, you probably already know this AMAZING YouTube channel "Cracking The Cryptic" (https://www.youtube.com/channel/UCC-UOdK8-mIjxBQm_ot1T-Q) where they do all kinds of crazy (and crazy hard) Sudoku variants.
A hidden skyscraper sudoku, where the outside clues indicate the first skyscraper that is hidden from that direction

Cheers and enjoy puzzling,
.dom
domz

Posts: 11
Joined: 16 September 2017

### Re: How to even get started on this skyscraper sudoku?

Hi domz

Thank you for that hidden skyscraper concept.

I create a lot Sky Scraper Sum (SSS) puzzles normally in ORC format (Odd Row Column - where even rows and columns can repeat and there are no nonets, but also NC, FNC and AK). Solutions often have "slums", i.e. low Skyscrapers where the value cannot be deduced from the four sums that point to it. Hence extra clue types are needed, so far I have used the number of 3,4,5 cell repeats in the solution which is unsatisfactory as it is only a lock-down of the final solution. A better approach was to create a number of killer cages with the same sum, all containing slums and the sum is unknown.

This might give me another approach which being skyscraper based is more fitting.

if you want to try them look up SSS and ORC on this site and the assassin one.

Maurice
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria