Wednesday, September 19, 2012

Circular growth


This is one of my latest inventions.
Shade some cells in a circular way starting from each clue,by choosing one of the upto eight neighbouring cells as the centre of the circle,and moving either clockwise or anti-clockwise, until that many cells are shaded,such that all shaded cells are orthogonally connected in the end.2x2 squares of all shaded cells are not allowed.Every clue should have exactly one circular growth.Circular growths from different clues often overlap.In the end, every shaded cell should belong to atleast one circular growth.



9 comments:

  1. I don't understand. Clockwise or anticlockwise from what reference point? What can that corner 5 possibly mean?

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  2. It means the direction around the centre ( the reference point). The centre,for example ,for the '5' would be R5C1 or R5C2 or R6C2.If you choose R5C2,you have two
    valid direcitons to choose from.And the growth would be a 'V' pentomino in both cases.A '3' could make either an 'I' or a 'V' trimino.A '4' can make only 'L'.

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    Replies
    1. OK, but some implications of that still make absolutely no sense.

      If "every clue should have exactly one circular growth," then the 2 must touch exactly one other shaded square. Then that second square can't touch anything else, since the clue says 2 and a third square would fit the pattern of a larger growth. So I'm describing an isolated domino, except that "all shaded cells are orthogonally connected."

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  3. Needless to mention, you cannot satisfy such perfect growths,while having a correct puzzle within the ruleset.As this was pretty obvious when i thought out this puzzle type, i did not add this point explicitly to the instructions.anything that is N or N+m long,is considered as a growth of N or longer.the point here is to have a growth that can place the clue within the puzzle successfully.

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  4. I don't understand either. An example puzzle with solution could be really useful.

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  5. I agree with boing; a picture is worth 1000 words.

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  6. Added a picture.If the instructions could not explain,i am not sure if a picture can help.You can think of a growth as shading of connected cells along an upto 8-cell ring starting from the clue cell,without branching off.
    In the picture,the grey cells on the left are valid.For the 5,if grey cells are used,then the red cells are not allowed,as they form another circular growth(around R4C4).If you use the red cells,the blue cell(R4C2) cannot be used to complete the solution,as it does not belong to any of the two growths.You can still find atleast 10 ways to satisfy all the rules.

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  7. I get that bit, but the original puzzle does not seem solvable.

    ROT13: Svyyvat pbyhza 5 ebj 6 znxrf gur 2 pyhr vzcbffvoyr. Svyyvat ebj 5 pbyhza 6 znxrf gur 4 pyhr vzcbffvoyr jvgubhg pbagenqvpgvat gur 2 nf jryy.

    I totally understand the way you're intending the rings to be made, I guess I'm just not fully understanding how the rings interact with one another. And while I hate for you to spoil your first puzzle, it would honestly be great if you did a post walking your readers through the puzzle step by step and explaining the logic behind it, and then allow us to fully understand it so that we may enjoy future puzzles of the type.

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  8. R5C3 in the intended solution violates a rule.Apologies, its unsolvable.

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