Introducing Benoku

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Re: Introducing Benoku

Postby Mathimagics » Tue Aug 20, 2019 8:57 am

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

I think he has got you there, Leren! 8-)
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Re: Introducing Benoku

Postby Leren » Tue Aug 20, 2019 11:01 am

Actually I got myself by not reading the Benoku rules. I've now changed my puzzle on the previous page to one that should hopefully be Benuko compliant.

Anyway, here is the original puzzle, which I'll now dub Lerenoku :D . The rules are the same as for Benoku, except that a blank black cell stays blank. This makes for a slightly more Str8ts compliant puzzle type. It's up to you to figure out which digit is missing in each row and column in which a blank black cell appears. Non-blank black cells are also allowed.

Code: Select all
  0    0    0    0    0    0    0    0    9 
  0    3    0    0    0    0    0   [0]   0 
  0    0    0    0    0    4    0    0    0 
  0    0    0   [0]   7    0    0    0    0 
  7    0    0    0    0    8    0    0    0 
  0   [0]   0    0    0    0    0    5    0 
  0    0    0    0    0    0    5    0    0 
  0    0    6    0    0    2    0    0    0 
  0    0    3    0    0    0   [0]   0    0 

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Last edited by Leren on Tue Aug 20, 2019 11:17 am, edited 1 time in total.
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Re: Introducing Benoku

Postby SCLT » Tue Aug 20, 2019 11:15 am

The new Benoku-compliant puzzle solves using only basics:

Hidden Text: Show
Code: Select all
+-----------+-----------+-------------+
| 7   2   5 |  9   1  6 |  3    8   4 |
| 6   3   4 |  8   5  2 |  7   [9]  1 |
| 9   1   8 |  7   3  4 |  2    5   6 |
+-----------+-----------+-------------+
| 3   4   2 | [1]  7  5 |  8    6   9 |
| 1   5   7 |  6   8  9 |  4    3   2 |
| 8  [9]  6 |  2   4  3 |  5    1   7 |
+-----------+-----------+-------------+
| 2   8   9 |  5   6  7 |  1    4   3 |
| 4   7   1 |  3   9  8 |  6    2   5 |
| 5   6   3 |  4   2  1 | [9]   7   8 |
+-----------+-----------+-------------+
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Re: Introducing Benoku

Postby Leren » Tue Aug 20, 2019 11:26 am

Hi SCLT,

Yes, I had to do a quick fix after reading the Benoku rules, so the puzzle was easy. You might like to try my Lerenoku puzzle above (I really should call this variant Str8tsB, but this is supposed to be a Sudoku forum). It's a bit more challenging.

For a really tough challenge try this Lerenoku puzzle.

Code: Select all
  0    0    3    0    0    0    0    0    0 
  0    0    0    5    0    0   [0]   0    0 
  0    0    0    0    0   [0]   0    0    0 
  6    0    0    0    0    0    0    0    7 
  0    0    0    0    0    0    8    0    0 
 [0]   0    1    0    3    0    0    4    0 
  0    0    0    0   [0]   0    0    0    0 
  0   [0]   6    0    0    0    0    0    0 
  3    0    0    4    0    0    0    5   [0]

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Re: Introducing Benoku

Postby SpAce » Tue Aug 20, 2019 12:10 pm

Leren wrote:Actually I got myself by not reading the Benoku rules.

Of course. It would be preposterous to even think I could "get" a genius like you. Yet your excuse is actually worse than the alternative because that's not an accident. It's just arrogance. So is the fact that you don't bother to apologize for wasting other people's time, or to thank them for bringing the mistake to your attention. Nothing new there, though. I'm done with you and your puzzles, thank you.
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Re: Introducing Benoku

Postby SCLT » Tue Aug 20, 2019 7:42 pm

Unique solutions for both Lerenoku found by hand-solving. I'm afraid I didn't record my solving path for either puzzle, but I only used basic moves and a general observation about Lerenoku.

Lerenoku 1:

Hidden Text: Show
Code: Select all
+---------+---------+---------+
| 6  5  4 | 7  2  1 | 3  8  9 |
| 8  3  7 | 9  5  6 | 4  .  2 |
| 1  2  9 | 8  3  4 | 6  7  5 |
+---------+---------+---------+
| 3  4  2 | .  7  5 | 9  6  8 |
| 7  6  5 | 4  9  8 | 2  1  3 |
| 9  .  8 | 2  6  3 | 7  5  4 |
+---------+---------+---------+
| 2  7  1 | 3  8  9 | 5  4  6 |
| 4  9  6 | 5  1  2 | 8  3  7 |
| 5  8  3 | 6  4  7 | .  2  1 |
+---------+---------+---------+


Lerenoku 2:

Hidden Text: Show
Code: Select all
+---------+---------+---------+
| 8  7  3 | 9  4  2 | 1  6  5 |
| 4  1  2 | 5  6  3 | .  7  8 |
| 5  6  9 | 8  7  . | 4  2  3 |
+---------+---------+---------+
| 6  5  8 | 1  2  4 | 3  9  7 |
| 7  3  4 | 6  5  9 | 8  1  2 |
| .  2  1 | 7  3  8 | 5  4  6 |
+---------+---------+---------+
| 2  4  5 | 3  .  7 | 6  8  9 |
| 1  .  6 | 2  8  5 | 7  3  4 |
| 3  8  7 | 4  9  6 | 2  5  . |
+---------+---------+---------+


I actually found the second puzzle easier than the first, although that may be because by that point I was used to the Lerenoku style. Here's the Lerenoku-specific logic that proved crucial:

In any chute (stack), the numbers that are missing from each row (column) must be the same numbers that are missing from the 3x3 boxes in that chute (stack), although not necessarily in a way that corresponds to a consistent number missing from each black cell. By cross-referencing each box with a blank cell against the set of rows/columns in the same chute/stack, you can determine constraints on which numbers can or cannot be missing from a given 3x3 box, and that opens up deductions which would not a priori be available.
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Re: Introducing Benoku

Postby SpAce » Fri Aug 23, 2019 12:04 am

SCLT wrote:Unique solutions for both Lerenoku found by hand-solving. I'm afraid I didn't record my solving path for either puzzle, but I only used basic moves and a general observation about Lerenoku.

I find that impressive. Personally I lack either the necessary IQ or the patience (or both) to solve these. The whole concept is just too unintuitive. I've had no problems with Blocku, Benoku (the fixed version), or Str8ts (now that I've looked into that too), but this melts my brain. My instincts are all off because it looks too much like a sudoku but isn't. It's also much harder to work with in Hodoku, which is a step backwards. My biggest gripe about Blocku was that it required slow p&p solving, but Benoku fixed that. This can also be entered into Hodoku, of course, but at some point the candidate maintenance gets difficult because the black cells can represent different digits for rows and columns.

That being said, let's face it that I just couldn't figure out a working process like you did, at least not in the time I was willing to put into it (now that I finally tried). Nice job! Also congrats to Leren for creating a puzzle type that beats me.
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Re: Introducing Benoku

Postby Leren » Fri Aug 23, 2019 8:01 am

Brilliant observation by SCLT. If all 3 rows in a tier, or columns in a stack, must contain a digit then a box must contain that digit, even if it has a grey cell. This enables you to build a table of required digits in grey cell boxes, increasing the chances of pointing intersections, and hidden tuples in boxes, and possibly more I haven't thought of yet. Whether this variant ends up being popular is another matter.

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Re: Introducing Benoku

Postby SCLT » Fri Aug 23, 2019 8:45 am

SpAce wrote:Personally I lack either the necessary IQ or the patience (or both) to solve these. The whole concept is just too unintuitive.


That's completely understandable.

Leaving aside the Str8ts-type compartment rule, Lerenoku is similar to a variant called "Blackout Sudoku" which occasionally appears on the competitive scene. Its rules are that each region must contain 8 distinct digits from 1-9 and a black cell, so "hidden" logic tends to fail because there are no regions that must contain every digit. It's often derided by those who take part in the competitions as being too unlike Sudoku, and too unintuitive to make a good competition puzzle.

The annoying thing about variants like this is that it's just too tempting to see hidden singles in places where they haven't been proven to exist yet!

In case you're at all interested, I re-solved the first Lerenoku puzzle and recorded my solution path. No promises that it's optimal, or that I didn't miss obvious steps or do things in the "wrong" order at any point. But if you have the time to follow through it it might help you to appreciate the logic behind the variant a bit more.

Hidden Text: Show
Code: Select all
Basic compartments: -3467r1c8, -4567r2c9, -5r123c4, -56r4c123, +23r4c123, -12r4c6789, +5r4c6, +6r4c789, -346r6c1, +789r789c2, -46r9c89

Row 4 and Row 6 must both contain a 6 --> Block 4 must contain a 6 --> +6r5c2

Compartments: -1c2

Column 2 missing a 1 --> Block 4 must also be missing a 1

Naked triples 234 r4c123, 689r4c789

Singles: +5r5c3, +3r4c1

Pointing 5b7: -5r123c1

Row 2 must contain 5 --> Block 3 contains 5 --> +5r3c9 --> +5r1c2 --> +5r2c5

Singles +2r3c2, +4r4c2, +2r4c3

Compartments and pair 89r6: +9r6c1, +8r6c3

Compartments: -1r6

Row 4 and Row 6 both missing 1 --> Block 5 must also be missing 1

Block 5 missing 1 --> Column 4 must be missing 1

Compartments: -23r123c4, +789r123c4, +23456r56789c4

Claiming 2b5: -2r56c5

Singles: +2r1c5, +9r5c5

Row 2 must contain 4 --> Block 3 must also contain 4

Pointing 4b3: -4r568c7

Block 3 contains a 9 --> Row 2 must contain a 9 --> -12r2c1234567

Singles (in order): +6r2c6, +3r6c6, +1r1c6, +3r3c5, +8r1c8, +7r1c4, +4r1c3, +6r1c1, +8r2c1, +1r3c1, +1r7c3, +9r2c4, +7r2c3, +9r3c3, +8r3c4, +4r2c7, +3r1c7

Compartments: -9c8

Column 8 missing a 9 and Block 3 contains a 9 --> Block 9 must be missing 9

Singles: +9r4c7, +6r4c8, +8r4c9, +9r8c2, +6r3c7, +7r3c8

Compartments: -1c7

Singles: +2r5c7, +7r6c7, +8r8c7, +4r6c9, +6r6c5, +2r6c4, +4r5c4

Row 9 must contain a 6 --> Block 9 must contain a 6 --> +6r7c9

Singles to the end
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Re: Introducing Benoku

Postby Leren » Fri Aug 23, 2019 11:13 am

Hi SCLT. There is a wealth of good information in your solution path. I'll try to improve the speed of my solver so that it more closely matches what a human solver would do.

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Re: Introducing Benoku

Postby koushanejad74 » Fri Aug 23, 2019 2:21 pm

Many thanks to all of you for posting comments, specially SCLT and Leren,

I'm working on a way that it shows the optimal way to solve the puzzle, any software programmer here who is willing to help? :roll:
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Re: Introducing Benoku

Postby SpAce » Fri Aug 23, 2019 7:58 pm

SCLT wrote:Leaving aside the Str8ts-type compartment rule, Lerenoku is similar to a variant called "Blackout Sudoku" which occasionally appears on the competitive scene. Its rules are that each region must contain 8 distinct digits from 1-9 and a black cell, so "hidden" logic tends to fail because there are no regions that must contain every digit. It's often derided by those who take part in the competitions as being too unlike Sudoku, and too unintuitive to make a good competition puzzle.

Thanks for that piece of information! Never heard of Blackout Sudoku before, but I'm not familiar with many variants anyway.

The annoying thing about variants like this is that it's just too tempting to see hidden singles in places where they haven't been proven to exist yet!

Exactly. Or, unless you're really certain about the rules and their implications, it might feel too scary to take even valid ones. That's kind of what happened to me.

In case you're at all interested, I re-solved the first Lerenoku puzzle and recorded my solution path. No promises that it's optimal, or that I didn't miss obvious steps or do things in the "wrong" order at any point. But if you have the time to follow through it it might help you to appreciate the logic behind the variant a bit more.

Thanks for that! I really appreciate it! Before I dive deeper into it, let me just make sure I understand the crucial bit:

Row 4 and Row 6 must both contain a 6 --> Block 4 must contain a 6 --> +6r5c2

I think I see that now. I didn't understand that part in your original post, but now it makes sense. You could make it even clearer by saying that explicit 6s are needed in both rows (as opposed to implicit ones within the black cells). I think the logic is also easier to understand if I focus on row 5, instead of box 4 (btw, "block" can be confused with the black cells, as in Blocku). Unlike box 4, row 5 doesn't have any black cells so it must contain all digits explicitly, which makes it easier to deal with. If we recognize the fact that neither black cell in r4 or r6 can represent a 6 row-wise (for different reasons), it leaves just r4c789 and r6c456 for 6s in those rows, and then claiming gives us a row-wise hidden single 6r5c2. Would you agree with that logic, and that it yields the same result? I'm sure yours works nicely and more quickly once internalized, but until then this POV might feel safer and more intuitive for me.

Perhaps it's conceptually wrong, but I still see the black cells as digits (or sets of candidates), though possibly different ones depending on the context (row, col, box). That's why I tried to maintain candidates within them, but color-coded to specify whether one applied to the row or col or both. It was a bit messy, but now that I might understand the logic a bit better, I think it might actually work that way too. I'll have to try again.
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Re: Introducing Benoku

Postby SCLT » Fri Aug 23, 2019 8:24 pm

SpAce wrote:Would you agree with that logic, and that it yields the same result?


Upon re-reading a couple of times, yes, I believe so. But I find it a bit uncomfortable, presumably in the same way my description is unintuitive to you. That's probably a result of you still seeing the black cells containing candidates, and me seeing them as completely empty - indeed, the first thing I do when solving one of these puzzles in something like Hodoku is to remove all candidates from the black cells.

Here's the clearest way (IMO) of explaining the logic from the POV of the black cells being completely empty. Looking row-wise, the middle tier must contain in total three 6s, because each row has one. Looking at the same cells box-wise instead of row-wise, there must therefore be one in each box.

(This same explanation generalises in the way that I pointed out originally to say that is S is the set (with repeats) of digits missing from the three rows/columns in a tier/stack, then the set of digits missing from the boxes in that same tier/stack must also be exactly S. I can't easily convince myself that your POV is as powerful, although maybe it is.)
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Re: Introducing Benoku

Postby Leren » Sat Aug 24, 2019 5:57 am

Well, after putting SLCT's Tier/Stack Box techniques into my SudokuB solver all of my puzzles now solve with basics. I would suggest that SudokuB is more constrained than Benoku because you always know the exact value of the black cell, whereas with Benoku there is some latitude there. With that in mind I've come up with a SudokuB puzzle that my solver uses more than basics. The trick ? Use the minimum of black cells.

Code: Select all
  0    0    0    6    0    0    0    0    0 
  0    5    0    4    0    0    7    0    0 
  0    0    0    0    0    9    0    3    5 
  7    0    2    0    0    0    5    0    0 
  0    0    0    0   [0]   0    0    0    0 
  0    0    4    0    0    0    0    8    0 
  6    0    0    0    0    0    0    0    0 
  1    0    0    0    0    0    2    0    0 
  0    0    0    0    0    3    4    9    0 

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