## Introducing Sudoku 7

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Introducing Sudoku 7

Sudoku 7 is a logic-based number-placement puzzle. It is distinct from but shares some properties and rules with Sudoku.
Rules:
• Every column must contain all the digits from 1 to 7
• Every gray cell and its 6 neighbors must contain all the digits from 1 to 7

Here's a sample with it's solution:

Problem:
Sudoku7ProblemIntro.png (51.44 KiB) Viewed 185 times

Solution:
Sudoku7SolutionIntro.png (62.89 KiB) Viewed 185 times

And here is an easy one to warm up:
Sudoku7_Sample001_Easy_Problem.png (51.5 KiB) Viewed 185 times

More challenging samples will be posted soon.
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sudoku 7

These do look interesting! It's a neat concept.

A suggestion - wrap your solution images with [hidden=Solution] tags ...

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Sudoku 7

Both have a valid single solution:

Solution:
Hidden Text: Show
Code: Select all
`  1   6   5  6 7 2 7 4 6 73 4 5 3 2 1 32 3 1 4 6 2 47 5 6 5 7 3 51 6 3 2 1 7 24 2 7 1 5 4 65   4   3   1`

Here are one's which requires locked singles:
Hidden Text: Show
Code: Select all
`  .   6   .  6 7 2 . . 6 .. . . 3 . . 3. 3 . 4 . . .7 . . 5 7 . 5. 6 . . . . 24 . . . . 4 .5   .   .   .  1   6   .  . . . . . 6 .3 . . 3 2 1 32 . . 4 . . 4. . . 5 . . .1 6 3 . . . 2. . 7 . . 4 ..   .   .   .`
creint

Posts: 146
Joined: 20 January 2018

### Re: Introducing Sudoku 7

That is lovely,

I'm sure you must have looked into the simpler rule "each line of hexagons can't have repeating numbers" which makes it very close to Hanidoku (avoid the consecutive rule). But that in addition to the grey cell and its neighbours having the same rule makes the puzzle very constrained and may not work.

Excellent work with the visuals and the ability to do it in text representation is good too.

tarek

tarek

Posts: 3352
Joined: 05 January 2006

### Re: Introducing Sudoku 7

Nice too from a software solver perspective - if you have a solver that can do arbitrary houses (like fsss2 then it is easily adapted to solve these ...

I see that creint has already got his (very) flexible solver onto it ...

BTW, I don't see a rule in the original post that adjacent cells must have different values, but surely this is a rule?

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Sudoku 7

Mathimagics wrote:Nice too from a software solver perspective - if you have a solver that can do arbitrary houses (like fsss2 then it is easily adapted to solve these ...

I see that creint has already got his (very) flexible solver onto it ...

BTW, I don't see a rule in the original post that adjacent cells must have different values, but surely this is a rule?

adjacent cells may have identical numbers as long as other rules are not violated
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sudoku 7

Thanks a ton guys for you comments,

I have a version where the diagonals with 7 cells form a group too, what do you think?
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sudoku 7

Generally speaking, adding additional houses can be good, but only up to a point.

Standard Sudoku is what I call a 3D puzzle, which just means that the cells are partitioned into complete houses (9 cells) in 3 ways (row, cols, boxes).

SudokuX is a 3.2D puzzle, 3 house partitions + 2 extra houses (the diagonals).

I think you can actually find somewhere in this section of the forum where I created a 6D puzzle!

Some general issues that apply are:

• Rendering: if the additional houses require specific identification (that is, are not intuitively obvious) then both image and printed forms of the puzzle have to be considered.

For example, SudokuW (aka Windoku), has a simple rendering solution, by using shading on the grid. SudokuP ("Disjoint Groups") can use colours when rendered on a screen, but actually needs no special handling at all, because the 9 "position in box" houses are intuitively obvious to most people. All you need to do really is LABEL the grid as a type SudokuP where this is not already clear.

• Solution space: each additional house reduces the solution grid space. This can be taken to excess, and make it harder to find valid solution grids from which to create your puzzles

• Solver experience: additional houses also allow you to produce puzzles that have few clues, and again, this can be taken to extremes. I remember someone (was it tarek?) discovering that 11-clue SudokuP puzzles (the minimum) tend to be much, much harder for P&P solving than a 17-clue vanilla Sudoku

Having said all that, your diagonals idea is most probably a good one!

It has none of these issues, and would probably be just as enjoyable as SudokuX is!

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Sudoku 7

koushanejad74 wrote:adjacent cells may have identical numbers as long as other rules are not violated

Ok, that's interesting.

The "no adjacent cells can have same value" rule is almost universal, so I think it would be wise to specify that this restriction does not apply in the list of rules! And perhaps use a puzzle with 2 adjacent clues having the same digit as your demonstration puzzle. You can't go wrong then ...

Is this restriction not applied because of the "solution space reduction" issue?

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Sudoku 7

Here's a sample where diagonal constraint is added,

Sudoku7_Sample002_Easy_Problem.png (96.26 KiB) Viewed 135 times
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sudoku 7

Here is an hard one:
Hidden Text: Show
Code: Select all
`  .   2   .  7 . . . . . 2. . . . . 6 .. . . . . . 3. . . . . . .. . . . . . .. 5 . . . 4 ..   .   .   .`
creint

Posts: 146
Joined: 20 January 2018

### Re: Introducing Sudoku 7

The simple rule of "non-repeating (or in other words: different) numbers in a line of hexagons" means 1-7 in a line of 7 hexagons. It can be extended to all lines even the smaller ones with less than 7. a line of 6 hexagons would have six different numbers out of the set 1,2,3,4,5,6,7

tarek

Posts: 3352
Joined: 05 January 2006

### Re: Introducing Sudoku 7

Good idea, tarek!

It would further reduce the set of solution grids, of course ...

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Sudoku 7

Tarek,

Actually that was my initial design, I'll post one like that soon,

Thanks,

-Kousha
koushanejad74

Posts: 75
Joined: 31 July 2019

### Re: Introducing Sudoku 7

Kousha,

I'd prefer it you don't draw lines through the diagonals!

You can simply indicate by rules, eg "All full-length diagonals have different digits", or "All diagonals have different digits" for Tarek's suggstion.

While I think of it, did you actually try the standard puzzle with the adjacent-cells-differ rule, and then found that it was hard (or impossible) to get solution grids?

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

Next

Return to Sudoku variants