The New Sudoku Players' Forum

[koushanejad74]

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 1179 times

Solution:

Sudoku7SolutionIntro.png (62.89 KiB) Viewed 1179 times

And here is an easy one to warm up:

Sudoku7_Sample001_Easy_Problem.png (51.5 KiB) Viewed 1179 times

More challenging samples will be posted soon.

[Mathimagics]

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

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

[creint]

Both have a valid single solution:

Solution:

Hidden Text: Show

Code: Select all

  1   6   5 
6 7 2 7 4 6 7
3 4 5 3 2 1 3
2 3 1 4 6 2 4
7 5 6 5 7 3 5
1 6 3 2 1 7 2
4 2 7 1 5 4 6
5   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 . . . . 2
4 . . . . 4 .
5   .   .   .

  1   6   . 
. . . . . 6 .
3 . . 3 2 1 3
2 . . 4 . . 4
. . . 5 . . .
1 6 3 . . . 2
. . 7 . . 4 .
.   .   .   .

[tarek]

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

[Mathimagics]

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?

[koushanejad74]

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]

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?

[Mathimagics]

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]

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?

[koushanejad74]

Here's a sample where diagonal constraint is added,

Sudoku7_Sample002_Easy_Problem.png (96.26 KiB) Viewed 1129 times

[creint]

Here is an hard one:

Hidden Text: Show

Code: Select all

  .   2   . 
7 . . . . . 2
. . . . . 6 .
. . . . . . 3
. . . . . . .
. . . . . . .
. 5 . . . 4 .
.   .   .   .

[tarek]

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

[Mathimagics]

Good idea, tarek!

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

[koushanejad74]

Tarek,

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

Thanks,

-Kousha

[Mathimagics]

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?