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Double CalcuDoku
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Posted on: Sat Dec 10, 2011 1:31 am

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: Double CalcuDoku
giulio wrote:
Again, I repost this from my blog http://giuliozambon.blogspot.com.
I can now generate Double CalcuDokus with any overlapping, although, at least for the time being, the overlapping region can only be a square. Here is an example of a 6x6 overlap:

I find puzzles with large overlaps more interesting. It makes it easier to exploit the fact that the cells of each row and columns that are not share must coincide. For example, in the above example, the three bottom cells of the middle column of the right puzzle include two singles: a 4 and a 2. This means that also the top three cells of the same column must include a 4 and a 2. As the 2-cell cage "9x" cannot possibly contain an even digit, it means that the they must be in the other two cells.

In my opinion the solution is clearly unique. The large overlap (36 cells) make it easy the final part of the solution once you have advanced considerably in the first, let's say the top left 9x9, calcudoku. The puzzle itself looks an interesting variation of the calcudoku, like the twin puzzles, etc. The difficulty is medium and the process of solution something between the double sudoku and the calcudoku (I think the samurai calcudoku will have the equivalent similarity to the samurai sudoku in the process of solution). This puzzle is undoubtedly much more easier than the corresponding 12x12 (that we would obtain if we would fill the top right and the bottom left "supressed" boxes of 3x3 cells) since, in the 12x12, the numbers go from 1 to 12 obviously and not only from 1 to 9. But, certainly, in this particular case, there is only one 5-cell cage, probably with bigger cages the difficulty would increase in this type of double 9x9's.

Extending the argument, in the case of the samurai calcudoku (I will look for time to solve the one in this thread) I think that the corresponding 21x21 (obtained by filling in the blank spaces) would also be of a much higher level of difficulty, obviously. But the same thing happens with the "sudokus", i.e., a 16x16 (from 1 to F) sudoku is much more difficult than a samurai sudoku.

One suggestion with the colours: to "shadow" the overlapped part (the 36 cells in this case) a little bit more than the rest, with slightly different colours, telling the puzzler the bounderies of that area, in some way underlining that area, though I understand that this is very subjective (other possibility is colouring the supressed boxes, the 9 cells in the top right and the 9 cells in the bottom left areas outside the puzzle).

Posted on: Sat Dec 10, 2011 4:57 am

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
sneaklyfox wrote:
Fun. Not hard, but takes some time. It might help to see the borders more clearly where the overlaps occur. Perhaps the overlapped cells could be coloured? I discovered two unresolved ambiguities. It would be better to have a unique solution. Ambiguities are in the bottom-left 9x9. Cells c1-d1, c8-d8. Also cells h1-i1, h3-i3.

You are right!
I thought my check for unicity was foolproof... It seems I'll have to work on it...

I agree with sneaklyfox and clm that the overlapping areas should be shaded. I'll do that.

Posted on: Mon Dec 12, 2011 2:40 am

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
giulio wrote:
sneaklyfox wrote:
[...] It would be better to have a unique solution. Ambiguities are in the bottom-left 9x9. Cells c1-d1, c8-d8. Also cells h1-i1, h3-i3.

You are right!
I thought my check for unicity was foolproof... It seems I'll have to work on it...

The problem was in the method that solves the puzzle by brute force. It had to be modified to be able to handle Samurai CalcuDokus. I was too eager to show the puzzle to you and was not careful enough. Sorry about that.

I fixed it but, in doing so, I realised that, while the method was OK with smaller puzzles, the combinatorial explosion of having 5*81-4*9 = 369 cells arranged in a 21x21 grid makes it completely impractical. I am now working at a different strategy. I'll keep you posted.

Posted on: Wed Dec 14, 2011 7:55 am

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
giulio wrote:
giulio wrote:
sneaklyfox wrote:
[...] It would be better to have a unique solution. Ambiguities are in the bottom-left 9x9. Cells c1-d1, c8-d8. Also cells h1-i1, h3-i3.

You are right!
I thought my check for unicity was foolproof... It seems I'll have to work on it...

The problem was in the method that solves the puzzle by brute force. It had to be modified to be able to handle Samurai CalcuDokus. I was too eager to show the puzzle to you and was not careful enough. Sorry about that.

I fixed it but, in doing so, I realised that, while the method was OK with smaller puzzles, the combinatorial explosion of having 5*81-4*9 = 369 cells arranged in a 21x21 grid makes it completely impractical. I am now working at a different strategy. I'll keep you posted.

To speed up the solving of puzzles, I simply rearranged the order in which the programs handles the cages. By keeping close together the cages of each one of the five squares that compose the Samurai CalcuDoku, I significantly reduced the amount of backtracking. In practical terms, I solved the five squares one after the other as much as I could. Obviously, it cannot be done 100%, because there are several cages that belong to two squares.

I thought I was done but, as soon as the test for uniqueness of the solution was in place, the program kept going forever. It never managed to create a puzzle without ambiguities. I let it run twice overnaight with two different ransom seeds, but it never managed to create a single puzzle with a unique solution. Don't ask me why, because I don't have a clue. I know that unique solutions are possible, but something in my generation algorithms prevents the program from converging. Odd.

I could fix that problem after noticing that sometimes the puzzle contained a single ambiguity consisting of two pairs of cells tat could be swapped, like the ambiguity that sneaklyfox discovered in my first Samurai CalcuDoku. I modified the program to accept solutions with one of such ambiguities and then to carve out from one of the pairs a single-cell cage. In that way, the program nails down one of the two alternatives and resolves the ambiguity.

I am curious concerning the fact that I can generate dozens of puzzles with a single ambiguity but none without any ambiguity, but I doubt that I would ever be able to find out why that happens...

[For once] I want to be pragmatic.

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