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PostPosted: Wed Mar 25, 2020 3:42 pm 
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Joined: Thu Nov 28, 2019 5:57 pm
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Tossing out some puzzles for people who are isolating and keeping safe. I wanted to pick something already popular and familiar based on the number of hits, and make them not too hard. This blog post is the result.

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For a few more, visit the blog here at Quadrata.


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PostPosted: Wed Mar 25, 2020 10:29 pm 
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Here is a bit of a different way to combine Sudoku with chess.

Note: In chess, the ranks are numbered from bottom to top, 1 through 8. The files are lettered a through h, left to right. In a normal chess game, the white pieces start on ranks 1-2 (at the bottom), the black pieces on ranks 7-8 (at the top).

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Starting with this position, fill the board with two complete chess sets of white and black pieces (2 kings, 2 queens, 4 bishops, 4 knights, 4 rooks, and 16 pawns of each color, 64 pieces total) in such a way that:

1. No king is in check.
2. There are no pawns on the first or eighth ranks.
3. There are exactly two white pawns and exactly two black pawns on each file, with each of the two white pawns occupying a lower-numbered rank than each of the two black pawns.
4. There are at most five white pawns on any rank, and at most five black pawns on any rank.
5. All pieces on the first and second ranks are white, and all pieces on the seventh and eighth ranks are black.
6. Of the four white bishops, two are on light squares and two are on dark squares, and similarly for the four black bishops.
7. No white rook is on the same rank or file as any black rook or black queen, and no black rook is on the same rank or file as any white rook or white queen.
8. No white bishop is on the same diagonal as any black bishop or black queen, and no black bishop is on the same diagonal as any white bishop or white queen.
9. No white queen is on the same rank, file, or diagonal as any black queen.
10. No white knight is a knight’s move away from any black knight.

Unless I’ve messed up, this puzzle has one, and only one, solution.

Bill Smythe


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PostPosted: Sat Mar 28, 2020 8:12 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 618
Bill

I'll try, but it will take time to get my head around all the rules. However I should not complain given some of my multi rule puzzles.

Maurice


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PostPosted: Sun Mar 29, 2020 4:40 pm 
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Joined: Mon Aug 20, 2012 5:03 am
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You're not supposed to complain, you're supposed to suffer. :twisted:

Hint: Start with rules 2 and 3 (the pawns). You will find that, on some files, that's already enough to locate all the pawns. And on some other files, it's almost enough.

Hint 2: Don't try to write a program that will solve the puzzle. You'll get there a lot faster if you simply work it out by hand. :| Oh my, how old-fashioned. :|

Bill Smythe


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