## Creating a BH-Sudoku

Everything about Sudoku that doesn't fit in one of the other sections

### Creating a BH-Sudoku

I am relatively new to Sudoku and I tried recently to construct my first one. I intend to send it to a friend whose initials are "BH", which is why I confined myself to the following form (0: no clue, x: clue):

000 000 000
xxx 00x 00x
x00 x0x 00x
x00 x0x 00x
xxx 00x xxx
x00 x0x 00x
x00 x0x 00x
xxx 00x 00x
000 000 000

I don't know if it is visible, but this pattern yields the letters "BH".

After several failed attempts I ended up with the following:

000 000 000
842 003 005
900 104 007
100 209 008
298 006 753
300 708 001
400 805 009
529 001 004
000 000 000

It has two solutions and I intend to fix this ambiguity by requiring verbally that somewhere in the solution the "lucky number" 13 has to appear (that is, a 1 followed in the same row by a 3 in the column to the right).

It is not very difficult to solve, but, I believe, also not especially easy. X-wing can give you a head start, but it is not needed.

Although for the purpose of sending this to my friend I am quite happy with the result, I became curious, so here are my questions:

1.) Is it possible to construct Sudokus with unique solutions with the pattern above? I strongly expect the answer to be yes, but since I did everything by hand eventually I gave up because construction by hand is a bit tedious after some time.

2.) Is it possible to construct the Sudoku in such a way that X-wing is needed for the 4 corners and the 6th column? I conjecture a "yes" but I am less sure here.

3.) Is it possible to make an irreducible Sudoku with the pattern above? (by "irreducible" I mean that you cannot remove any of the clues and still get a unique result).

4.) What is the "most difficult" Sudoku that can be constructed with the pattern above? Now, this question will not have a unique answer, but what I mean is, how complicated can one rearrange the clues without destroying the BH pattern? Apart from the X-wing technique that might be needed for the corners there is surely a lot that can be done with forcing chains in the 7th and 8th column.

Please let me know if you have answers to these questions, I appreciate any input.
Big Blue

Posts: 28
Joined: 01 August 2005

### Re: Creating a BH-Sudoku

Big Blue wrote:1.) Is it possible to construct Sudokus with unique solutions with the pattern above?

Yes. Here's an example, rated easy or moderate:

Code: Select all
`. . . . . . . . .2 6 3 . . 9 . . 51 . . 8 . 2 . . 33 . . 9 . 8 . . 77 9 5 . . 3 8 1 44 . . 1 . 5 . . 28 . . 3 . 6 . . 16 4 7 . . 1 . . 8. . . . . . . . .`

You can crank out as many as you want here.

Here's one created with this. You have to figure out how this works -- but you can create a template file that has your design and if there are enough clues, it'll crank out 100's at a time to your specifications. It also rates the puzzles difficulty, but I've found the ratings silly -- fiendish can are trivial. If you can't figure it out, send me a PM and I'll give more detail.
Code: Select all
` . . . . . . . . . 2 8 1 . . 4 . . 3 3 . . 1 . 2 . . 7 9 . . 4 . 7 . . 5 6 2 7 . . 5 3 4 1 5 . . 2 . 3 . . 8 1 . . 7 . 8 . . 2 4 9 5 . . 1 . . 6 . . . . . . . . .`

To try to judge difficulty: Pappocom's software will rate the puzzle, as will SadMan's solver. Paul's Pages has an online rater. Ratings will vary.

You have a lot of clues though -- 33. You might want to try with fewer.

Big Blue wrote:2.) Is it possible to construct the Sudoku in such a way that X-wing is needed for the 4 corners and the 6th column? I conjecture a "yes" but I am less sure here.

No idea. Probably.

Big Blue wrote:3.) Is it possible to make an irreducible Sudoku with the pattern above? (by "irreducible" I mean that you cannot remove any of the clues and still get a unique result).

Probably. 33 is a lot of clues though. Here's one with 27:

Code: Select all
`. . . . . . . . .. 7 3 . . 5 . . .9 . . 8 . 1 . . .4 . . 1 . 6 . . .1 . 7 . . 9 8 2 48 . . 2 . 4 . . 92 . . 9 . 3 . . 5. 8 9 . . 2 . . 3. . . . . . . . .`

Big Blue wrote:4.) What is the "most difficult" Sudoku that can be constructed with the pattern above? Now, this question will not have a unique answer, but what I mean is, how complicated can one rearrange the clues without destroying the BH pattern? Apart from the X-wing technique that might be needed for the corners there is surely a lot that can be done with forcing chains in the 7th and 8th column.

I don't know, but I assume there is no limit. You should be able to compose any structure using that pattern. I still haven't learned to compose -- start here.
tso

Posts: 798
Joined: 22 June 2005

I agree that 33 clues are many, probably too many for a Sudoku with a reasonable level of difficulty. However, I gave the aesthetics of the clue pattern prime importance.

Actually, I visited the tutorial for creating Sudokus that you mention in the link at the bottom of your reply before attempting my construction. I found it useful, but not crucial for this particular Sudoku. The main lesson I drew from the tutorial was that it is sound to try to finish, as far as possible, one particular number before starting on the next number during the construction.

In my particular Sudoku it was also very helpful that I decided a priori to use one number only once as a clue, because then I could delete a lot of options for that number.

Thanks also for the links to software - I downloaded the source files and I will try to install and compile them on my laptop.

However, I am a bit old fashioned when it comes to puzzles: I want to construct and to solve them by hand, not by computer - it spoils the fun for me, otherwise...

But for answering general Sudoku questions (like what is the minimal number of clues, 17, 16 or below?) I can see that this software is extremely useful.

So thanks again!
Big Blue

Posts: 28
Joined: 01 August 2005