SudokuSolver Forum

I have recently encountered a puzzle which is practically a one-dimensional version of Sudoku.

The puzzle goes like this - you're given a line of 27 cells, and the goal is to fill each cell with a value from 1 to 9. Each value must appear exactly 3 times, and the special constraint is there must be exactly n cells spaced between each cell holding value n.

To demonstrate this special constraint, let's try a smaller example: with a line of 6 cells, fill in the values 1 to 3, exactly twice for each. Then it seems the following is the only possible solution (barring reflection):
1 cell between the two 1s, 2 cells between the two 2s, 3 cells between the two 3s.

Another smaller example: with a line of 8 cells, fill in the values 1 to 4, exactly twice for each. Then the following should be the only possible solution (again, barring reflection):
1 cell between the two 1s, 2 cells between the two 2s, 3 cells between the two 3s, 4 cells between the two 4s.

So, I was told the following 3 puzzles each gives a unique solution, and these are essentially all the possible solution lines for the case of 3x9=27 cells (barring reflection):

Some questions:

1. Are these problems only solvable by computer programs? Is there any logical approach to find out the answer, or is T&E the only possible way?

2. If some more clues are given, can these puzzles be made more solvable to a competent human Sudoku player? If so, what is the minimum number of clues to make them "human solvable"?

3. Can this puzzle be generalised to a two-dimensional version? If so what are the new rules?

4. I've also been told that for the case of 3x10=30 cells, there are only 5 possible solution lines (barring reflection). But I don't have any idea on how to work them out. Can any programming guru help me out on this?

Thanks heaps in advance!

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ADYFNC HJPLI BVSM GgK Oa m

I have seen a kinda 2-dimensional version at the World puzzle championships. It was build up of circles using this principle. That was a fun puzzle.

For this puzzle, it just seems like a packing puzzle. Where you try to fit 9 pieces in.

Para

I'm interested to that WPC puzzle. Could you tell me more about it please?

As for your "packing" view I suggest you to visit this thread:

http://www.sudoku.com/boards/viewtopic.php?t=6375

I'll post more results in there later.

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ADYFNC HJPLI BVSM GgK Oa m

I can't actually post the puzzle, i think. Copyright issues and such. In each country the organisation that is a member of the WPF has the right to distribute them.

Basically there were 3 circles of 16 cells. They were crossing eachother so that the left and right circle shared two places with the middle. Then there were two smaller circles of 8 that were linked to one circle of the middle and both were situated in the middle of the left and right bigger circle.
So then the idea was to place 2 numbers of 1-8 in the big circle and 2 of 1-4 in the smaller, with the rule that there had to be n cells between 2 digits n in one direction. This puzzle had a bunch of givens and was pretty fun to solve, all logically deductable.

Thanks for the reply Para. I was just curious about the puzzle, really no time to try it out. So I think I'll give it a pass (and skip the scrutinising on your mystic descriptions ).

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ADYFNC HJPLI BVSM GgK Oa m

Lol. Explaining puzzles without pictures is not easy .