Anti-knight sudoku

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Anti-knight sudoku

Postby MichalStajszczak » Sat Aug 26, 2006 10:36 am

I have prepared a new (I hope) variant of sudoku: "anti-knight sudoku".
(First published on www.mathpuzzle.com this week)

Image

It is standard sudoku with one more condition: the same numbers are not "knight move connected".
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Postby udosuk » Sat Aug 26, 2006 10:43 am

Thanks, we discussed about this feature in this thread last year... But we didn't actually made a puzzle... So well done!:)
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Postby Pyrrhon » Sat Aug 26, 2006 12:25 pm

There is a similar variant out called White Knight Sudoku (exemple) where this constraint is only for the 9's which are substituted by knights.

BTW: There is also a Black Knight Sudoku (example) out where every 9 (knight) must be supported by another knight. And there are also Queen and Knight Sudoku (example).

I remember also a White Queen Sudoku and a Black Queen sudoku where the 9's are substituted by chess Queens and the rest is the same, i. e., in White Queen Sudoku in every diagonal (partial diagonals included) can be at most one 9 (queen). But I'm not aware where I saw this variants.
Last edited by Pyrrhon on Sat Aug 26, 2006 10:10 am, edited 2 times in total.
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Postby MichalStajszczak » Sat Aug 26, 2006 12:29 pm

The next step is sudoku anti-knight and diagonal:

Image

It has very curious feature, which one can see examining numbers in this diagram, but is valid for all numbers in the solution
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Postby Smythe Dakota » Sat Aug 26, 2006 11:52 pm

If we're playing sudoku with chess rules, maybe we could also play chess with sudoku rules.

Play chess on a 9x9 board, with nine pawns on each player's second rank, and with an extra piece between the king and queen.

A knight move can be defined as a move to one of the nearest squares which is not on the same rank, file, or diagonal as the starting square.

Likewise, the move of a sudoku-knight (the extra piece mentioned above) could be defined as a move to one of the nearest squares which is not on the same rank, file, diagonal, or box as the starting square.

In most cases, a sudoku-knight would be less powerful than a knight, as all sudoku-knight moves would be knight moves, but not vice versa.

However, with the above definition, a sudoku-knight in one of the corner squares (say r1c1) would have two possible moves (in this case r4c2 and r2c4), neither of which would be knight moves.

Unfortunately, though, a sudoku-knight could never get to one of the corner squares to begin with.

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Postby udosuk » Sun Aug 27, 2006 9:33 am

MichalStajszczak wrote:It has very curious feature, which one can see examining numbers in this diagram, but is valid for all numbers in the solution

That feature was discussed in this thread, and gurth invented a technique about it called "gurth's symmetrical placement", for which ravel has produced some puzzles in here... Also, I have posted 2 variants having that feature in here...

BTW nice puzzles... Enjoyed solving them...:)
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Postby MichalStajszczak » Sun Aug 27, 2006 11:03 am

udosuk wrote:
That feature was discussed

Are you sure?
I mean such feature:
Let S(i,j) is a number in i-row and j-column
For each i and j in my puzzle S(i,j)+S(10-i,10-j)=10
For example: the third (from the left) number in the first row + the third (from the right) number in the last row = 10
This valid for all 41 pairs, including S(5,5)+S(5,5)=10
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Postby udosuk » Sun Aug 27, 2006 12:01 pm

Yes, exactly the same feature I'm talking about...

Although in general, you can permute the values after this property is established... So in fact we just need 4 pairs of values, so that each value is mirrored by it's partner across the centre point, or itself if it happens to be the sole value, which must be the one on r5c5...

Formal definition of gurth's symmetrical placement wrote:Let the 9 values be a1,a2,b1,b2,c1,c2,d1,d2,e.

In the initial setup of a puzzle, if each of r[i]c[j] and r[10-i]c[10-j] are {a1,a2} or {b1,b2} or {c1,c2} or {d1,d2} or {e,e} or both empty, and r5c5 is {e} or empty,

then all other cells must all have this property.
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Postby Smythe Dakota » Sun Aug 27, 2006 1:07 pm

MichalStajszczak wrote:The next step is sudoku anti-knight and diagonal:

Image

....

Clarification, please.

If by "diagonal" you mean ANY diagonal, not just the longest diagonals (r1c1-r9c9 and r1c9-r9c1) then there is no solution, as there is no cell in the upper middle box where a 9 can go.

Or maybe you intended to outlaw only diagonally ADJACENT same digits.

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Re: Anti-knight sudoku

Postby Smythe Dakota » Sun Aug 27, 2006 1:12 pm

MichalStajszczak wrote:I have prepared a new (I hope) variant of sudoku: "anti-knight sudoku". ....

Image

....

Nice puzzle. I was stuck for a long time about halfway through, until I realized that r3c1 could not be a 4 because that would preclude 4's in both r4c1 and r4c3. Once I saw that, the rest came quickly.

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Postby udosuk » Sun Aug 27, 2006 1:26 pm

Smythe Dakota wrote:Clarification, please.

If by "diagonal" you mean ANY diagonal, not just the longest diagonals (r1c1-r9c9 and r1c9-r9c1) then there is no solution, as there is no cell in the upper middle box where a 9 can go.

Or maybe you intended to outlaw only diagonally ADJACENT same digits.

No, it's just no repetition on the 2 main (longest) diagonals...

Generally we call these puzzles "Sudoku X", and would draw a light-coloured "X" on the background of the grid... So this particular puzzle could be coined a "Anti-knight Sudoku X"...

It has been verified that it's impossible to have all the digits not repeated on all diagonals. See this thread and this thread. The closest thing you can get is no repetition for 7 of 9 values...
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Postby MichalStajszczak » Sun Aug 27, 2006 4:12 pm

udosuk wrote:
Yes, exactly the same feature I'm talking about...

You are right. My puzzle is the special case, where:
e=5 and a1+a2=b1+b2=c1+c2=d1+d2=10
My goal was to prepare Anti-knight Sudoku X and I was very surprised by its symmetry
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Postby Smythe Dakota » Mon Aug 28, 2006 5:31 am

udosuk wrote:.... No, it's just no repetition on the 2 main (longest) diagonals ....

Thanks. I guess, with the knight and all, I was in chess mode, so interpreted "diagonal" as queen.

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Postby Pyrrhon » Mon Aug 28, 2006 7:08 am

I want make an overview about crossovers between chess and sudoku.

1-player

  • Chess Sudoku (The digits 1-8 and a chess piece in each row, column, and region. Each piece should attack the numbers 1-8 exactly once. (proposal, discussion and examples)
  • Slightly Modified Chess Sudoku (The digits 1-8 and a chess piece in each row, column, and region. Each piece can attack the numbers 1-8 exactly once.)
  • White Knight Sudoku (9 Knights) (each row, column and box contains the digits 1-8, a white chess knight, no white knight attacks one other knight) (example, other example)
  • White Knight Sudoku (18 Knights) (each row, column and box contains the digits 1-7, two white chess knights, no white knight attacks one other knight) (example)
  • Black Knight Sudoku (9 Knights) (each row, column and box contains the digits 1-8 and a black chess knight, every knight attacks at least one other) (example, other example)
  • Black Knight Sudoku (18 Knights) (each row, column and box contains the digits 1-7 and two black chess knights, every knight attacks at least one other) (example, other example)
  • Black and White Knight Sudoku (each row, column and box contains the digits 1-7, a black chess knight and a white chess knight, every black knight attacks at least one other black knight, no white knight attacks one other white knight) (example)
  • Knight and Queen Sudoku (each row, column and box contains the digits 1-8 and a white chess knight or a white queen (one per puzzle), no chess piece attacks one other) (example)
  • (White) Queen Sudoku (each row, column and box contains the digits 1-8, and a white chess queen, no white queen attacks one other queen) (example)
  • Bishop Sudoku (each row, column and box contains the digits 1-8 and a black chess bishop, every bishop attacks at least one other) (example)
  • Anti-Knight Sudoku (each row, column and box contains the digits 1-9, no digit is knight-move connected with the same digit) (example, other example)
  • Anti-Knight Sudoku X (each row, column, box and both main diagonals contain the digits 1-9, no digit is knight-move connected with the same digit) (example)
  • Knight Non-Consecutive Sudoku (each row, column and box contains the digits 1-9, no digit is knight-move connected with a consecutive digit) (examples and discussion)
  • Chess related Zero Killer Sudoku X (example and discussion)
  • Sudoku with chess piece pattern (example)
  • Perfect Knight Sudoku (rules and example)
  • Knight Tour Latin Square (examples)
  • Knight Tour Sudoku 25 (example)
  • Horsudoku example

2-player


Hints to other chess sudoku crossover are welcome.
Last edited by Pyrrhon on Thu Feb 21, 2008 7:26 am, edited 2 times in total.
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Postby Pyrrhon » Tue Sep 05, 2006 8:10 am

I've updated the list.

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