## Sumoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Sumoku

I've searched EVERYWHERE online and I can't seem to find these puzzles. Please please please add them to your site.

Here are the game rules if you're unsure what the actually game is:

In these puzzles, the completed diagrams will include each of the numbers from 1 to 9 in the squares of every row and column. Your only clues are provided in the little rectangles within the diagram. They indicate the sum of the digits they contain. Determine the correct number for each square.

I love love love this game! I first played it in my puzzle book Sudoku Variety Volume 4. They are only 18 Sumoku puzzles in this book though.
cherryblossom

Posts: 1
Joined: 17 April 2009

you mean, what The Times calls "Killer Sudoku" ?

Pat

Posts: 3880
Joined: 18 July 2005

### Re: Sumoku

I think this is what she is talking about? I was looking for some strategy for the game when I found this post.

All I've figured out so far is; each row ads to 45 (1+2+3+4+5+6+7+8+9= 45) and the little blocks with 3 or 4 have only one possible answer 2+1 and 3+1 and of course the inverse 1+2 and 1+3. 5 thru 17 have more possible.
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GoldToyBox

Posts: 1
Joined: 31 December 2015

### Re: Sumoku

That is indeed "Killer Sudoku" - see Wiki entry(Killer Sudoku).

Mathimagics
2017 Supporter

Posts: 1485
Joined: 27 May 2015
Location: Canberra

### Re: Sumoku

I don't think this is "Killer Sudoku" because I have checked Kappa Book Sudoku Plus #295 and at least one of them is, by its listed solution, correctly solved _without_ using Nonets. I only have three Kappa books, but none of the "Sumokus" use Nonets, and neither does GoldToyBox's picture.
carls.haven

Posts: 5
Joined: 16 March 2016

### Re: Sumoku

Hi all,

If there is no nonet restriction but the line restriction still applies then it is a "killer latin square" because sudoku is Latin Square + nonet

You can call it KLS or Killer LS or whatever name you like as long as the underlying principle is easily conveyed.

tarek

tarek

Posts: 3531
Joined: 05 January 2006

### Re: Sumoku

In your photo, all of the jigsaw pieces consist of only 2 cells, except for one that has 3 cells.

In some I have seen, some jigsaw pieces consist of 4 cells, 5 cells, or even more. And the pieces needn't be rectangles. For example, a 4-cell piece could consist of r1c1, r2c1, r2c2, and r3c2.

Bill Smythe
Smythe Dakota

Posts: 563
Joined: 11 February 2006

### Re: Sumoku

Okay, so;
Sumoku in The Times is http://puzwiki.com/index.php/Killer_Sudoku (thanks Pat)
and
Sumoku in Kappa Books is http://puzwiki.com/index.php/Killer_Latin_Square (thanks tarek)
is this agreeable?
carls.haven

Posts: 5
Joined: 16 March 2016

carls.haven wrote:Okay, so;
Sumoku in The Times is http://puzwiki.com/index.php/Killer_Sudoku (thanks Pat)
and
Sumoku in Kappa Books is http://puzwiki.com/index.php/Killer_Latin_Square (thanks tarek)
is this agreeable?

sorry, my mistake,
already in the original post it says "every row and column"
( no mention of boxes ),
likewise in image provided by GoldToyBox

the puzzles in The Times
do also have boxes

Pat

Posts: 3880
Joined: 18 July 2005

Smythe Dakota wrote:
the pieces needn't be rectangles.

For example, a 4-cell piece
could consist of r1c1, r2c1, r2c2, and r3c2.

and the range would be
6-34
OR add a rule of no-repeat-within-cage,
then the range is reduced to the familiar
10-30

Pat

Posts: 3880
Joined: 18 July 2005

### Re: Sumoku

carls.haven wrote:Okay, so;
Sumoku in The Times is http://puzwiki.com/index.php/Killer_Sudoku (thanks Pat)
and
Sumoku in Kappa Books is http://puzwiki.com/index.php/Killer_Latin_Square (thanks tarek)
is this agreeable?

tarek

Posts: 3531
Joined: 05 January 2006

### Re: Sumoku

Who would have thought it would take 7 years from the original question to straighten that out lol! Thanks all, as I am happy that I now know for sure which is which. However, as I am new to "Killer"s (both kinds lol,) Pat could you please elaborate on your reply to Smythe Dakota? I understand the basics but I don't understand what you are explaining.
edit; forgot how to count apparently lol
carls.haven

Posts: 5
Joined: 16 March 2016

### Re: Sumoku

carls.haven wrote: .... Pat could you please elaborate on your reply to Smythe Dakota? ....

I think Pat just means that, within a 4-cell cage, if all four cells are in the same row or column, then (to avoid duplicate digits in the row or column) the minimum 4-digit sum is 1+2+3+4 which is 10, and the maximum is 9+8+7+6 which is 30.

The same would be true even if the four cells are not all in the same line, as long as you add a no-repeat-within-cage rule.

Without such a rule, the minimum would be 1+1+1+1 which is 4, and the maximum would be 9+9+9+9 which is 36.

However, if you invoke a rule that a cage must be rook-connected, then you'll find that it is not possible to have a 4-cell cage whose cells are all in different rows (or different columns). Therefore (try it!), even without a no-repeat-within-cage rule, the minimum is 1+2+1+2 which is 6, and the maximum is 9+8+9+8 which is 34, as long as you still have the no-repeat-within-row and no-repeat-within column rules.

By "rook-connected" I mean that it must be possible to travel from any cell in the cage to any other cell in the cage, staying within the cage, with a sequence of 1-cell horizontal and vertical movements. This is a standard constraint that almost everybody invokes in all these kinds of variations. No disconnected cages (like the Hawaiian Islands) allowed!

I think the three (or more) variations put forth in this thread are all based on the same general idea (cages), but have different constraints. Still another such variation is the jigsaw Sudoku, where instead of having nine 3x3 boxes you have nine 9-cell cages (irregularly shaped but each cage is rook-connected), with no-repeat-within rules applied to rows, columns, and cages, rather than to rows, columns, and boxes. I even saw a 7-by-7 version once (digits 1 through 7), where the cages could not be boxes because 7 is a prime number.

Bill Smythe
Smythe Dakota

Posts: 563
Joined: 11 February 2006

### Re: Sumoku

Ah, yes, that makes sense, thank you!
carls.haven

Posts: 5
Joined: 16 March 2016

### Re: Sumoku

When you think about it & see the original Killer Sudokus published in the times that had sum cages that do not allow number repetition, then you can see that the 9x9 Vanilla sudoku is nothing but a Killer Latin square (with 9 non intersecting 3x3 boxes of sum 45)

tarek

tarek

Posts: 3531
Joined: 05 January 2006

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