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The "chained" puzzles
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Posted on: Thu Jan 24, 2013 10:35 pm

Posts: 713
Joined: Fri May 13, 2011 6:51 pm
The "chained" puzzles
The chained puzzles.

The idea is as follows: We initially solve the “left” puzzle (first puzzle in the chain) finding some necessary numbers, the values of some individual cells (three, four, five, … , cells), required to fill the “blank” cells in the “right” puzzle (second puzzle in the chain); this second puzzle can not be solved without that information. Applying the same concept, the chain may have as many puzzles (2, 3, 4, 5, … ) of the same size as we like though, typically, it would consist of two puzzles (but, for instance, a chain of four 6x6 puzzles could be dessigned for books, etc., since they could be drawn in a page). The solution is reached when all puzzles in the chain are solved.

It is possible to have “chained” puzzles of any size, the level of difficulty depending on the structure of the puzzles themselves, as usual, and on the number of “blank” cells in the successive puzzles (obviously this number could vary each time we enter a new puzzle in the chain).

For the example below, the “prototype”, I have used the Jan 22, 2013, 6x6 medium modified by a “replacement” (solution unique verified, though this modification converts it probably in an easy puzzle) for the “left” puzzle and the Jan 22, 2013 6x6 difficult (4 blank cells in this example) for the right puzzle. A medium-difficult 6x6 chained puzzles could score 7 points, for instance, while a pair of difficult-difficult 6x6 chained puzzles could score 9 points. A very difficult-very difficult 9x9 (like the Tuesday’s 9x9’s, for instance) chained puzzles could score 14 or 16 points, etc..

“Left” puzzle (first to solve):

“Right puzzle” (second in the chain):

Posted on: Fri Jan 25, 2013 6:47 am

Posts: 98
Joined: Fri May 13, 2011 12:48 am
Re: The "chained" puzzles
Interesting idea clm. I like it. What do you think of the idea of nesting chains? For example a 4x4 inside a 6x6(taking up the middles spaces) which is than inside of an 8x8, etc. It might be a little more difficult to implement.

Posted on: Fri Jan 25, 2013 12:18 pm

Posts: 713
Joined: Fri May 13, 2011 6:51 pm
Re: The "chained" puzzles
picklepep wrote:
Interesting idea clm. I like it. What do you think of the idea of nesting chains? For example a 4x4 inside a 6x6(taking up the middles spaces) which is than inside of an 8x8, etc. It might be a little more difficult to implement.

Hi, picklepep, thanks for your comments, your idea for the "nested" calcudokus, in an "increasing" chain, is a good idea and perfectly feasible I think (though I do not know about the difficulties of programming these concepts, let's see the Patrick's comments ). In fact, a 4x4 nested in a 6x6, i.e., in the easy level, could open the imagination and skill of the new calcudokers. In the other hand, i.e., a typical 6x6 difficult inside a 10x10 with mod function or bitwise OR cages in the outside border would be a curious challenge.

In the case of the "nested" puzzles it would be necessary to solve first the inner part, right?, to detemine the required (and overlapped) cells to continue solving the wider puzzle. For this purpose I would suggest the use of colours to define the areas so that no additional bolded lines (other than those for the cages) would be required.

BTW, the KSudoku looks in some way a very particular case of your idea, each nonet is part of a wider structure and provides essential information to the contiguous nonets ... , here the use of two sets of colours to define the nonets and the cages does not look very compatible, that's why the standard solution is that the nonets, as in the regular Sudoku, are defined with bolded lines and the cages with dotted lines and/or colours (depending on the creators); both, the dotted lines or colours, much better than the continuous lines, make more confortable the presentation.

Posted on: Fri Jan 25, 2013 2:48 pm

Posts: 2295
Joined: Thu May 12, 2011 11:58 pm
Re: The "chained" puzzles
Yes, it is interesting, and closely related to the twin puzzle (ideally you'd
want twin puzzles that are not solvable by themselves).

The 2nd puzzle with the clues filled in, though, simply becomes a puzzle
with those clues as singles, right?

Patrick

Posted on: Fri Jan 25, 2013 10:07 pm

Posts: 713
Joined: Fri May 13, 2011 6:51 pm
Re: The "chained" puzzles
pnm wrote:
Yes, it is interesting, and closely related to the twin puzzle (ideally you'd
want twin puzzles that are not solvable by themselves).

The 2nd puzzle with the clues filled in, though, simply becomes a puzzle
with those clues as singles, right?

Patrick

Yes, Patrick, that's the idea, the clues are the single cells in the second (or successive puzzles) and the clues must be determined in the first puzzle (or "previous" puzzle, "left", in the chain).

The difference is that with the twin you can work both simultaneously while in the "chained" (and possibly in the "nested" as proposed by picklepep) normally it would be necessary to completely solve first the "left" (or inner in the picklepep proposal) puzzle because until you have all clues you could not start (well apart of some operations and candidates here and there) the second puzzle with guarantees. In the twin you finish both simultaneously (they are interleaved) while in the "chained" you solve them in sequence (they are absolutely independent, that is the structure of the cages and distribution of numbers would be absolutely different): The twin have the same aspect (with different dresses ) while the "chained" puzzles (with different aspect) are "linked" by a few cells, let's say, a marriage .

Apparently it's not difficult to program, right?.

Posted on: Fri Jan 25, 2013 10:18 pm

Posts: 2295
Joined: Thu May 12, 2011 11:58 pm
Re: The "chained" puzzles
clm wrote:
Apparently it's not difficult to program, right?.

I think it's doable. It made me think of a way on how to determine when
a puzzle is no longer solvable, thanks

(but note that doable not necessarily == "takes little time" )

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