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 Hard patterns 
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Posted on: Wed Apr 11, 2012 8:26 am




Posts: 31
Joined: Mon Mar 05, 2012 10:45 am
Post Re: Hard patterns
The "differences only" puzzles are difficult and require usually lots of guesswork to solve. Maybe the rating should be adjusted somehow to reflect this fact.


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Posted on: Wed Apr 11, 2012 1:41 pm




Posts: 248
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 3:40 pm
Post Re: Hard patterns
Hello, Clm.
I was the Easter week on holidays without calcudoku ( online ) and I completed my puzzles books ( offline ). I also used it to study your solution to the 8x8 puzzle ( 22MAR2012 ) that I thank you again. It's a very interesting method, very smart and clever. I learned something more. It's a pity it can't be applied at all these puzzles ( Module ). The uncovered independence of the columns d-e is the basis of that elegant solution and posterior already normal solution.After that I solved a similar puzzle from the books that took me several hours and many " trials and errors " ).
Thanks to one or two colleagues ( I think it was Sneaklyfox and ( or ) Starling ) I began to use the Paint to solve the puzzles. It saves me paper, pencil and principally ink and time. But it must there be another program similar but better, because Clm present us with his diagrams with the numbers well centered and well put in the cell ( centered, or in a low position or in a high position ). Is there indeed another program or has Paint some particularities I don't know?

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Posted on: Wed Apr 11, 2012 5:13 pm




Posts: 576
Joined: Fri May 13, 2011 4:51 pm
Post Re: Hard patterns
jomapil wrote:
Hello, Clm.
I was the Easter week on holidays without calcudoku ( online ) and I completed my puzzles books ( offline ). I also used it to study your solution to the 8x8 puzzle ( 22MAR2012 ) that I thank you again. It's a very interesting method, very smart and clever. I learned something more. It's a pity it can't be applied at all these puzzles ( Module ). The uncovered independence of the columns d-e is the basis of that elegant solution and posterior already normal solution.After that I solved a similar puzzle from the books that took me several hours and many " trials and errors " ).
Thanks to one or two colleagues ( I think it was Sneaklyfox and ( or ) Starling ) I began to use the Paint to solve the puzzles. It saves me paper, pencil and principally ink and time. But it must there be another program similar but better, because Clm present us with his diagrams with the numbers well centered and well put in the cell ( centered, or in a low position or in a high position ). Is there indeed another program or has Paint some particularities I don't know?


You are very welcome, jomapil. The very difficult puzzles are always the more interesting and challenging, every puzzle is different and unique of course, but all have a weaker point (in an analytical sense) from where to start the solution (sometimes more than one point so producing several ways to the solution) sometimes we must observe them deeply to find those weak points (having in mind the main tips and rules). I would like to find a demonstration for my previous affirmation (thread - "A 6x6: Is the analysis enough to solve a calcudoku?"): "If a calcudoku has a unique solution, it can be solved using only analytical means", let's say an easy demonstration, using only the logic, for instance, to convert it in a theorem; there is always a reason why every number must be in a determined place and only in that place.

With respect to the graphics I prefer using the Paint (it's handy for me to draw sketches or building the diagrams and the .png files do not occupy much), I find it creative, though a little slow. But, for solving the puzzles, if you have the "Micro$ Office" package, for instance, the Excel (or even the PowerPoint) have adequate features, though I am sure many puzzlers here have more advanced tools.


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Posted on: Wed Apr 11, 2012 5:39 pm




Posts: 31
Joined: Mon Mar 05, 2012 10:45 am
Post Re: Hard patterns
Well, in order to prove your theorem, you need first to defne "analytical means". The definition is not at all obvious: I, for one, say that I have solved a puzzle analytically, if never had to enter a number on the diagram, not being sure that it belongs exactly it this place. However, while not writing anything down, in my mind I often build hypotheses like: "if I put this number here, there would be contradiction". Then "if I put this number here, then this would have to go here, then there will be contradiction". Then "if I put this here, then this would have to go here, then this would have to be here, then contradiction"... You see the pattern. I personally find, that I can keep in my mind locatons of about 5 numbers before getting lost and having to put the numbers down in writing rather than just imagining them. But obviously someone with better memory would be able to "store" longer sequences, thus have a better chance of solving a puzzle analytically in this sense.

So, what is your definition of analytical solution?


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Posted on: Wed Apr 11, 2012 5:45 pm




Posts: 1480
Joined: Thu May 12, 2011 9:58 pm
Post Re: Hard patterns
jotempe wrote:
Well, in order to prove your theorem, you need first to defne "analytical means".

I think intuitively you could argue that
- a Calcudoku puzzle is in fact a large set of conditions on, say, 36 variables (for a 6x6), with a single solution
- because there's a single solution, there must be either a condition with a single unknown, or such a condition
can be derived from a set of existing condtions
- etc. [bored]

Patrick


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Posted on: Wed Apr 11, 2012 6:23 pm




Posts: 576
Joined: Fri May 13, 2011 4:51 pm
Post Re: Hard patterns
pnm wrote:
jotempe wrote:
Well, in order to prove your theorem, you need first to defne "analytical means".

I think intuitively you could argue that
- a Calcudoku puzzle is in fact a large set of conditions on, say, 36 variables (for a 6x6), with a single solution
- because there's a single solution, there must be either a condition with a single unknown, or such a condition
can be derived from a set of existing condtions
- etc. [bored]

Patrick


By "analytical means" I understand the full set of tools we actually have (the addition and multiplication of numbers in a line, the parity rule, maximums and minimums, etc.) and other that we may develop in the future as long as they are exact and true conditions.

Yes, Patrick, that's exactly the kind of reasoning I would like to follow, using the premises as a logical "filter".

Anytime someone "guesses" and arrives to a an impossibility we could go backwards and, "looking to the future", "analytically" suppress that line (the chess players, i.e, though "seing" in advance many movements, cann't do this because there is not an end, there is a practically "infinite" number of ways and games, I found in a book of "Chess and Mathematics" a calculation according to which, with only the first 20 movements for whites and 20 for blacks, writing the games in a very slim, 0,01 mm, sheets of paper, making books and placing them in a library 100 bookcases high, the light would need 1 million years to travel around the library), here we have a finite number of lines and operations to follow.


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Posted on: Tue Apr 17, 2012 2:44 pm




Posts: 248
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 3:40 pm
Post Re: Hard patterns
The pattern of today is one of the more difficult. With so many combinations it took me 4H30M to complete.
This is a diagram I think it's not possible to finish without some or many " trial and error ".

P.S. - By any reason it is 15H40M TMG ( GMT ? ) and only 34 players have completed so far.

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Posted on: Tue Apr 17, 2012 6:01 pm




Posts: 109
Joined: Fri Jun 17, 2011 6:15 pm
Post Re: Hard patterns
jomapil wrote:
This is a diagram I think it's not possible to finish without some or many " trial and error ".


I used every trick I've learned short of guessing - including a longer than usual lunch break - but I finished this puzzle without trial and error. I guess often enough - almost always with the subtraction only puzzles, it seems. But today's 9x9 I managed to avoid that. I did a lot of summing across three and four rows or columns.

Not trying to brag - it took me 19 hours after the puzzle was first available to reach the solution - just saying that it is possible.


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Posted on: Fri Apr 20, 2012 8:06 pm




Posts: 576
Joined: Fri May 13, 2011 4:51 pm
Post Re: Hard patterns
jomapil wrote:
The pattern of today is one of the more difficult. With so many combinations it took me 4H30M to complete.
This is a diagram I think it's not possible to finish without some or many " trial and error ".

P.S. - By any reason it is 15H40M TMG ( GMT ? ) and only 34 players have completed so far.


I am sending a post to the section “Solving strategies and tips” with a full solution, step by step, for this type of 9x9 puzzle. I think it is possible to use only “analytical means” as explained in the post.

jaek wrote:
jomapil wrote:
This is a diagram I think it's not possible to finish without some or many " trial and error ".


I used every trick I've learned short of guessing - including a longer than usual lunch break - but I finished this puzzle without trial and error. I guess often enough - almost always with the subtraction only puzzles, it seems. But today's 9x9 I managed to avoid that. I did a lot of summing across three and four rows or columns.

Not trying to brag - it took me 19 hours after the puzzle was first available to reach the solution - just saying that it is possible.


Perhaps you did the same sums (three columns or four rows) I show in the solution process, I am absolutely in favour of the analyical ways. It is a little tedious but it should not take so many hours (if we choose the appropriate key cells).


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Posted on: Tue Jul 24, 2012 8:53 am




Posts: 7
Joined: Sat May 26, 2012 5:09 pm
Post Re: Hard patterns
Today's 9x9 is probably one of the most difficult puzzles I've encountered! Just wanted to say congratulations to all the solvers who completed it. I give up temporarily after 1 1/2 hour but I don't think I can solve this pattern. So many combinations...!


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