## Introducing Benoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Introducing Benoku

Benoku is a logic-based number-placement puzzle. It is distinct from but shares some properties and rules with Str8ts and Sudoku.
Rules:
• All sudoku rules apply.
• Some rows and columns are divided into two compartments by a gray cell
• Each compartment, vertically or horizontally, must contain a straight – a set of consecutive numbers, but in any order. For example: 7, 6, 4, 5 is valid, but 1, 3, 8, 7 is not.

Benoku_Easy_001.png (16.16 KiB) Viewed 312 times

Benoku Definition
Benoku Sample (Easy)

Posts: 75
Joined: 31 July 2019

### Re: Introducing Benoku

Your rules as stated are ambiguous and confusing, or maybe I'm too stupid to understand them. Furthermore, even if I make some assumptions about them (like that a gray cell must be either 1 or 9 and actually part of one or the other compartment), I can't solve even this "easy" example. Can you show a walk-through of the logic you're expecting to be used here?

Here's as far as I get with basic techniques (or anything I'm willing to do anyway):

Code: Select all
`.-----------------.------------------------.---------------------.|  2     78   9   | 1       345    345     | 345     6       78  ||  3     678  567 | 24579   4578   24589   | 1245    1245    789 || [1]    4    57  | 2579    6      23589   | 235     235     789 |:-----------------+------------------------+---------------------:|  467   567  3   | 45679   2      45689   | 45679   4578   [1]  ||  467   567  12  | 45679   34578  1345689 | 245679  24578   245 ||  8    [9]   12  | 4567    457    1456    | 24567   2457    3   |:-----------------+------------------------+---------------------:|  9     1    8   | 2456    45     2456    | 37      37      245 ||  5     2    4   | 3      [1]     7       | 8       9       6   ||  67    3    67  | 8       9      245     | 1245    1245    245 |'-----------------'------------------------'---------------------'`

Have I made mistakes? If not, how do you proceed from there? It seems to me that all the compartment rules have already been exhausted, so it's just vanilla sudoku rules left -- and with just those this is not possible to solve. (Or more accurately, it has over 500 solutions according to SudokuWiki, so it can't be solved logically. The same thing with your other example in the Definition page. I'm thinking the published solution must be just one of many. Did you ever check that?)

What am I missing? It must be something obvious since you call this easy... And please don't give me a similar non-answer as you did here. I'm still awaiting a further explanation for that puzzle as well.

PS. I'm starting to suspect that you don't even check that your puzzles have a single solution. If so, that's simply unforgivable, because nothing is more frustrating for a manual solver (except maybe that a puzzle has no solution at all). It's already been clear that you don't have a proper way to assess the difficulty of your puzzles because you don't have a solver that uses logical techniques. That's annoying too but less severe. At the very least you should have a brute force solver that checks for multiple solutions before you publish anything. Until you address this suspicion, I won't be trying more of your puzzles.

SpAce

Posts: 2016
Joined: 22 May 2017

### Re: Introducing Benoku

SpAce,

you completeley misunderstood that.
There is no claim, that the puzzles would have a unique solution. They are easy, because almost every guess leaves a valid solution
eleven

Posts: 2223
Joined: 10 February 2008

### Re: Introducing Benoku

eleven wrote:SpAce,

you completeley misunderstood that.
There is no claim, that the puzzles would have a unique solution. They are easy, because almost every guess leaves a valid solution

SpAce

Posts: 2016
Joined: 22 May 2017

### Re: Introducing Benoku

eleven wrote:SpAce,

you completeley misunderstood that.
There is no claim, that the puzzles would have a unique solution. They are easy, because almost every guess leaves a valid solution

Eleven,

Although I didn't mention it, the puzzle MUST have a unique solution, have you found more than one solution?

Thanks,

-Kousha

Posts: 75
Joined: 31 July 2019

### Re: Introducing Benoku

The puzzle provided in the example (Benoku Definition) has multiple solutions, or at least I don't see why any of those would be invalid.
Here are two more solutions, and there may be more.

Code: Select all
`+-------+----------+----------+| 4 3 5 |  9 67 67 | 18  2 18 || 8 9 7 |  1  2  3 |  6  4  5 || 2 1 6 |  8  4  5 |  9  3  7 |+-------+----------+----------+| 6 4 9 |  7  1  8 |  3  5  2 || 5 7 8 | 36 36  2 |  4  1  9 || 3 2 1 |  5  9  4 | 78 78  6 |+-------+----------+----------+| 7 5 3 | 46  8 16 |  2  9 14 || 9 8 4 |  2  5 17 | 17  6  3 || 1 6 2 | 34 37  9 |  5 78 48 |+-------+----------+----------+`

Image: Show
Wecoc

Posts: 70
Joined: 08 April 2019
Location: Girona, Catalonia

### Re: Introducing Benoku

Agreed! The rules seem clear and not ambiguous, but nevertheless SpAce is correct with his puzzle state as listed above. There are many ways to complete it.

Wecoc has found a similar problem with the linked example.

So either the rules are missing some vital extra constraint, or the puzzle examples as presented are ambiguous. If the poster is using software to generate and/or check them, then I suggest that software is dodgy ...

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Benoku

I liked the Blocku variant better because of 2 reasons:
- In this one all blocks must be given, which spoils the chance for harder puzzles like in the other one
- While trying to solve the example, I noticed the candidates on the cells with blocks are very limited

They can only be 19, except for 5 coordinates in the entire grid:
Code: Select all
`+-------+---------------+-------+| . . . |   .   .   .   | . . . || . . . |   .   .   .   | . . . || . . . |   .   .   .   | . . . |+-------+---------------+-------+| . . . | 1469  .  1469 | . . . || . . . |   .  159  .   | . . . || . . . | 1469  .  1469 | . . . |+-------+---------------+-------+| . . . |   .   .   .   | . . . || . . . |   .   .   .   | . . . || . . . |   .   .   .   | . . . |+-------+---------------+-------+`

I did a fast check with my solver on the other idea I gave about adapting the Blocku rules on a Sudoku grid using 9s as blocks. As far as I tried it looks like it's impossible.
As I said, the constrain with consecutive digits on both sides (and both axis) is too restrictive, and adding the 3x3 box rule it always results on a crash.
Wecoc

Posts: 70
Joined: 08 April 2019
Location: Girona, Catalonia

### Re: Introducing Benoku

My apologies, specially to space
I'm afraid I've posted the wrong one, the algorithm I have ensures the solution is unique, I even tried it on paper before posting it, but then I uploaded another one. will correct it soon,

Posts: 75
Joined: 31 July 2019

### Re: Introducing Benoku

In the meantime, if I understand Benoku correctly you can make the solution unique by adding two extra clues : 4 in r5c5 & 6 in r5c7. The puzzle is easy to solve and the unique solution is

Code: Select all
`289135467376482159045769328463528970751943682802671543918256734524307896637894215`

The 57's in r67c57 are OK, because he says that all Sudoku rules apply, so Box 8 can't have two 7's' and Box 9 can't have two 5's.

Leren
Leren

Posts: 3720
Joined: 03 June 2012

### Re: Introducing Benoku

Confirmed. Nice job, Leren!!

Mathimagics
2017 Supporter

Posts: 1480
Joined: 27 May 2015
Location: Canberra

### Re: Introducing Benoku

Well, seeing as I appear to be on a roll here, you can also add r3c5 & r6c5 = 5 for a unique solution

Code: Select all
`289135467365974218047268359473629580651783924802451673918546732524307896736892145`

This one appears to be harder to solve, requiring some chaining, or some UR moves, if I'm not mistaken.

Leren
Leren

Posts: 3720
Joined: 03 June 2012

### Re: Introducing Benoku

As promised, a corrected sample has been posted here
{Benoku (Part II) -- URL corrected by Moderator}

Posts: 75
Joined: 31 July 2019

### Re: Introducing Benoku

For some reason I can't get koushanejad74's here link to work. In the meantime here is my own Benoku puzzle.

Code: Select all
`  7    0    0    0    1    0    0    0    0    0    3    0    0    0    0    0   [0]   0    0    0    0    0    0    4    0    0    0    0    0    0   [0]   0    0    0    0    0    1    0    0    0    0    9    0    0    2    0   [0]   0    2    0    0    0    0    0    2    0    0    0    6    7    0    0    3    0    0    0    0    0    0    0    2    0    0    0    0    0    0    0   [0]   0    0 `

Leren

<Edit> Improved drawing style of puzzle and changed to be Benoku compliant.
Last edited by Leren on Tue Aug 20, 2019 10:56 am, edited 2 times in total.
Leren

Posts: 3720
Joined: 03 June 2012

### Re: Introducing Benoku

Leren wrote:
Code: Select all
`........9.3.....X......4......X7....7....8....X.....5.......5....6..2.....3...X..`

What have I missed if I don't understand what can go in r2c8?

SpAce

Posts: 2016
Joined: 22 May 2017

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