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Using 'Unique Solution' to help solve
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Posted on: Fri May 10, 2013 5:15 pm

Posts: 4
Joined: Fri May 10, 2013 7:39 am
Using 'Unique Solution' to help solve
What do you think about this? Sometimes you can use the assumption/fact that there is a unique solution to a calcudoku to eliminate possibilities. Is this a valid solving strategy? Is it cheating? Does it diminish the accomplishment of solving the puzzle? Should you believe the puzzle you're working on has a unique solution before you've solved it?

Thanks for the feedback

Posted on: Fri May 10, 2013 5:40 pm

Posts: 2238
Joined: Thu May 12, 2011 11:58 pm
Re: Using 'Unique Solution' to help solve
It took some digging, but there was a similar question at some point:
viewtopic.php?f=2&t=76

Definitely a valid solving strategy in my opinion, because you know the puzzle has a unique solution.

Patrick

Posted on: Sat May 11, 2013 12:10 am

Posts: 93
Joined: Sat May 14, 2011 1:08 am
Re: Using 'Unique Solution' to help solve
Back in the early days of this site puzzles didn't always have unique solutions, so that trained me to avoid using the assumption of a unique solution as a solving strategy. That hasn't been the case for years, but old habits die hard.

As far as "cheating" is concerned, I think you have to make up your own mind as to what you want to accomplish. For example: is using a calculator cheating? I personally don't use one because I want to give myself more practice doing arithmetic. I do use notepad to avoid wasting scratch paper, but no other tools ... with the exception of the continuous error checking function, which on occasion I will use with trial and error to determine possibilities, especially for exponentiation cases -- go figure.

Posted on: Sat May 11, 2013 1:47 pm

Posts: 698
Joined: Fri May 13, 2011 6:51 pm
Re: Using 'Unique Solution' to help solve
tommyp0123 wrote:
... Is this a valid solving strategy? ...

Thanks for the feedback

Really, in my opinion, it's not a solving strategy itself, but you deal with these situations sometimes and it's a valid "tactic" to progress and you can "gain time" in the solution process, based in the assumption that the solution is unique. In the other hand, in fact, it's not strictly necessary to use that since you will arrive anyway to the same conclusion if you solve other parts of the puzzle by eliminating the wrong possibilities using the analysis. I have found, i.e., in "good", advanced Suduku books, puzzles with more than one solution, by transposing numbers, producing two or four different solutions, certainly very few times, but sometimes; and in the "bad" books you can find "many" solutions, an even number of solutions: two ... four ... n! - n factorial, which is even if n >= 2.

As stronger is the software as bigger is the probability of the unique solution (in the numeric puzzles). The Patrick's software has reached a great degree of consistency after a few million Calcudokus and many modifications to make it more robust, so you can be confident when making that assumption. However, "theorically", we must accept some "really small" probability that a Calcudoku has more than one solution, let's say, 1 in 10,000,000 ?, or 1 in 100,000,000, or perhaps 1 in 1,000,000,000 ? . When a new type of puzzle (new function, etc.) is being implemented (introduced) the wrong situations can happen, only in the initial phase (like when the KSudokus were being developed, at that time even some violations of the non-duplication rule inside the cages occurred ...).

Posted on: Sat May 11, 2013 2:50 pm

Posts: 2238
Joined: Thu May 12, 2011 11:58 pm
Re: Using 'Unique Solution' to help solve
clm wrote:
As stronger is the software as bigger is the probability of the unique solution (in the numeric puzzles). The Patrick's software has reached a great degree of consistency after a few million Calcudokus and many modifications to make it more robust, so you can be confident when making that assumption. However, "theorically", we must accept some "really small" probability that a Calcudoku has more than one solution, let's say, 1 in 10,000,000 ?, or 1 in 100,000,000, or perhaps 1 in 1,000,000,000 ?

I think by now it must be possible to mathematically prove that my current program always produces a puzzle with a single solution
clm wrote:
When a new type of puzzle (new function, etc.) is being implemented (introduced) the wrong situations can happen, only in the initial phase (like when the KSudokus were being developed, at that time even some violations of the non-duplication rule inside the cages occurred ...).

True, but initially this was intentional (I thought it was still optional,
whereas in reality it is accepted that cages also must not have duplicates)

Posted on: Sat May 11, 2013 6:38 pm

Posts: 4
Joined: Fri May 10, 2013 7:39 am
Re: Using 'Unique Solution' to help solve
I do calcudoku for the enjoyment and the satisfaction. When I'm solving one I fill in a square when I know what it must be. If I rule out possibilities based on the assumption that the solution is unique do I really know what the square must be? (I'm talking about all calcudoku puzzles, not just Patrick's) Am I denying myself the opportunity to discover some new technique or insight? To sharpen my skill? Does it affect my level satisfaction?

My answer is yes, it detracts from the experience and I don't use it 'prove' anything.

When calcudokus get boring to me I'll stop doing them (and I've done hundreds and hundreds over the last couple of years). When I start using the unique solution assumption I'll know that I really just want to be done with the puzzle and I'm not really enjoying the experience.

Posted on: Sat May 11, 2013 7:41 pm

Posts: 98
Joined: Fri May 13, 2011 12:48 am
Re: Using 'Unique Solution' to help solve
tommyp0123 wrote:
I do calcudoku for the enjoyment and the satisfaction. When I'm solving one I fill in a square when I know what it must be. If I rule out possibilities based on the assumption that the solution is unique do I really know what the square must be? (I'm talking about all calcudoku puzzles, not just Patrick's) Am I denying myself the opportunity to discover some new technique or insight? To sharpen my skill? Does it affect my level satisfaction?

My answer is yes, it detracts from the experience and I don't use it 'prove' anything.

When calcudokus get boring to me I'll stop doing them (and I've done hundreds and hundreds over the last couple of years). When I start using the unique solution assumption I'll know that I really just want to be done with the puzzle and I'm not really enjoying the experience.

I disagree. The unique solution is a criteria and a stricture to these puzzles. It is a given much like that of there only being one iteration of a number in a row or column. I don't believe in self-imposed limits when we are solving these puzzles. To do so would limit my ability to sharpen my skill, or gain insight in the way the numbers work together.

I can think of a few puzzles where if I hadn't used this method the only alternative would have been the old 'trial and error'. Now if I had an alternative between using two methods, one of which was plugging in numbers, and the other which required me to think, I'm going to use the one that sharpens my acumen.

Posted on: Sun May 12, 2013 11:40 am

Posts: 2238
Joined: Thu May 12, 2011 11:58 pm
Re: Using 'Unique Solution' to help solve
picklepep wrote:
I disagree. The unique solution is a criteria and a stricture to these puzzles. It is a given much like that of there only being one iteration of a number in a row or column. I don't believe in self-imposed limits when we are solving these puzzles. To do so would limit my ability to sharpen my skill, or gain insight in the way the numbers work together.

I agree with picklepep: the fact that a puzzle has a unique solution is simply another rule/restriction
that can be used to solve the puzzle, like any of the others.

Posted on: Sun May 12, 2013 8:23 pm

Posts: 4
Joined: Fri May 10, 2013 7:39 am
Re: Using 'Unique Solution' to help solve
picklepep wrote:
I disagree. The unique solution is a criteria and a stricture to these puzzles. It is a given much like that of there only being one iteration of a number in a row or column. I don't believe in self-imposed limits when we are solving these puzzles. To do so would limit my ability to sharpen my skill, or gain insight in the way the numbers work together.

I can think of a few puzzles where if I hadn't used this method the only alternative would have been the old 'trial and error'. Now if I had an alternative between using two methods, one of which was plugging in numbers, and the other which required me to think, I'm going to use the one that sharpens my acumen.

I respect that. It's been my experience that I have always found a way to proceed using technique and not brute-force.

Posted on: Sun May 12, 2013 10:33 pm

Posts: 13
Joined: Sun Mar 04, 2012 6:46 pm
Re: Using 'Unique Solution' to help solve
tommyp0123 wrote:
picklepep wrote:
I disagree. The unique solution is a criteria and a stricture to these puzzles. It is a given much like that of there only being one iteration of a number in a row or column. I don't believe in self-imposed limits when we are solving these puzzles. To do so would limit my ability to sharpen my skill, or gain insight in the way the numbers work together.

I can think of a few puzzles where if I hadn't used this method the only alternative would have been the old 'trial and error'. Now if I had an alternative between using two methods, one of which was plugging in numbers, and the other which required me to think, I'm going to use the one that sharpens my acumen.

I respect that. It's been my experience that I have always found a way to proceed using technique and not brute-force.

I would not call "making use of the uniqueness of the solution" brute force. It's just a piece of info one has from the start. And it's even impossible not to use this if one ends up spotting that a certain combination of numbers cannot be right as otherwise the solution would not be unique. It's not something one can "unlearn on demand".

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