incoherency solver

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Vince Fernando
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incoherency solver

Post by Vince Fernando » Wed Aug 15, 2018 8:26 pm

Does the incoherency number solver give all possible solutions?

Owen Carroll
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Re: incoherency solver

Post by Owen Carroll » Wed Aug 15, 2018 8:47 pm

Vince Fernando wrote:
Wed Aug 15, 2018 8:26 pm
Does the incoherency number solver give all possible solutions?
Yep.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Sat Aug 18, 2018 11:40 am

Owen Carroll:
Do you have any evidence to back your claim?

Owen Carroll
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Re: incoherency solver

Post by Owen Carroll » Sat Aug 18, 2018 8:45 pm

Vince Fernando wrote:
Sat Aug 18, 2018 11:40 am
Owen Carroll:
Do you have any evidence to back your claim?
I've used it a lot to practise for the show. It gives all possible solutions.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Tue Aug 21, 2018 6:59 pm

Owen Carroll:
Why are you so certain that the incoherency solver gives all possible solutions to a given problem? I presume that you have not analysed each and every problem.

Elliott Mellor
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Re: incoherency solver

Post by Elliott Mellor » Tue Aug 21, 2018 7:35 pm

Vince Fernando wrote:
Tue Aug 21, 2018 6:59 pm
Owen Carroll:
Why are you so certain that the incoherency solver gives all possible solutions to a given problem? I presume that you have not analysed each and every problem.
Of course he hasn't analysed every single problem - he hasn't the time and nor has anyone. I can safely say that the numbers solver will give the closest solution possible every time due to the code it has been programmed with. It won't give every solution though as for stuff like 100 8 5 2 6 10 @110 there would clearly be far too many to list.

Owen Carroll
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Re: incoherency solver

Post by Owen Carroll » Tue Aug 21, 2018 9:51 pm

Elliott's right. When I said all possible solutions I meant the closest solution it can get to, if it can't get right on.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Tue Aug 21, 2018 10:32 pm

What Elliott Mellor says is a reasonable outcome from a good solver. However, it is not meaningful to equal "all possible solutions" to "the closest solution" as Owen Carroll has stated.

Suppose that there are just four solutions (avoiding trivial equivalent solutions due to commutative properties, i.e. a+b = b+a, a*b = b*a ), does the solver gives all 4 solutions?

Gavin Chipper
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Re: incoherency solver

Post by Gavin Chipper » Tue Aug 21, 2018 10:39 pm

Vince Fernando wrote:
Tue Aug 21, 2018 10:32 pm
What Elliott Mellor says is a reasonable outcome from a good solver. However, it is not meaningful to equal "all possible solutions" to "the closest solution" as Owen Carroll has stated.

Suppose that there are just four solutions (avoiding trivial equivalent solutions due to commutative properties, i.e. a+b = b+a, a*b = b*a ), does the solver gives all 4 solutions?
I think you're opening a whole can of worms talking about what counts as equivalent solutions though.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Tue Aug 21, 2018 11:23 pm

Gavin Chipper:

Thanks for the pointer to the "can of worms". I do not wish to re-open this "can of worms" but the equivalence problem is not exactly "rocket science"; any competent mathematician should be able to solve the problem.

Going back to the incoherency solver, suppose that there are "too many" non-trivial solutions. Does anybody know how many is "too many"?

Elliott Mellor
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Re: incoherency solver

Post by Elliott Mellor » Wed Aug 22, 2018 7:47 am

Vince Fernando wrote:
Tue Aug 21, 2018 11:23 pm
Gavin Chipper:

Thanks for the pointer to the "can of worms". I do not wish to re-open this "can of worms" but the equivalence problem is not exactly "rocket science"; any competent mathematician should be able to solve the problem.

Going back to the incoherency solver, suppose that there are "too many" non-trivial solutions. Does anybody know how many is "too many"?
More than 1. It will only ever give 1 solution regardless of whether there is 2 solutions or 200 solutions.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Wed Aug 22, 2018 11:45 am

Elliott Mellor:
"More than 1. It will only ever give 1 solution regardless of whether there is 2 solutions or 200 solutions."

I do not understand your statement. I have seen up to six alternative solutions from the incoherency solver.

Gavin Chipper
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Re: incoherency solver

Post by Gavin Chipper » Wed Aug 22, 2018 12:14 pm

Vince Fernando wrote:
Tue Aug 21, 2018 11:23 pm
Gavin Chipper:

Thanks for the pointer to the "can of worms". I do not wish to re-open this "can of worms" but the equivalence problem is not exactly "rocket science"; any competent mathematician should be able to solve the problem.
Maybe they could, but then another mathematician could solve the problem and come up with a different answer. The point is that it's partly subjective.

Elliott Mellor
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Re: incoherency solver

Post by Elliott Mellor » Wed Aug 22, 2018 1:06 pm

Vince Fernando wrote:
Wed Aug 22, 2018 11:45 am
Elliott Mellor:
"More than 1. It will only ever give 1 solution regardless of whether there is 2 solutions or 200 solutions."

I do not understand your statement. I have seen up to six alternative solutions from the incoherency solver.
I've never really cared that much about it, but from any times I've used the solver it has only ever given one solution - perhaps you're thinking of a different solver.

Elliott Mellor
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Re: incoherency solver

Post by Elliott Mellor » Wed Aug 22, 2018 1:07 pm

Gavin Chipper wrote:
Wed Aug 22, 2018 12:14 pm
Vince Fernando wrote:
Tue Aug 21, 2018 11:23 pm
Gavin Chipper:

Thanks for the pointer to the "can of worms". I do not wish to re-open this "can of worms" but the equivalence problem is not exactly "rocket science"; any competent mathematician should be able to solve the problem.
Maybe they could, but then another mathematician could solve the problem and come up with a different answer. The point is that it's partly subjective.
This. I'd say 100*5+10 is the same solution as 5*100+10 but not the same as 5*100+4+6, but opinion on this differs.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Wed Aug 22, 2018 2:18 pm

Gavin Chipper:
Elliot Mellor:

I am using the incoherency solver and it often gives more than one solution. My original question was whether the solution set is complete. If incoherency gives only one answer then my question is not a meaningful question in the first place.

Mathematics is never considered as subjective. If a different mathematician gets another solution then the initial axioms used by these two mathematicians are obviously different. If they use the same playing field then the results have to be identical.

5*100+10 is obviously different from 5*100+4+6 since there are 3 and 4 integers, respectively.

Elliott Mellor
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Re: incoherency solver

Post by Elliott Mellor » Wed Aug 22, 2018 3:05 pm

I've just checked and it actually seems you are now right, it does give more than one solution. However I am certain this never used to be the case. It seems the solution set is complete - I just typed in a set of numbers and target that should give loads of solutions and indeed it gave me a heck of a lot.

Also, if you're going to bother about something like this can you bother to spell my name correctly?

Gavin Chipper
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Re: incoherency solver

Post by Gavin Chipper » Wed Aug 22, 2018 6:02 pm

Vince Fernando wrote:
Wed Aug 22, 2018 2:18 pm
Gavin Chipper:
Elliot Mellor:

I am using the incoherency solver and it often gives more than one solution. My original question was whether the solution set is complete. If incoherency gives only one answer then my question is not a meaningful question in the first place.

Mathematics is never considered as subjective. If a different mathematician gets another solution then the initial axioms used by these two mathematicians are obviously different. If they use the same playing field then the results have to be identical.

5*100+10 is obviously different from 5*100+4+6 since there are 3 and 4 integers, respectively.
Then in this case they might be using different axioms, because by asking which numbers solutions in Countdown are identical, you're not formally defining it.

Fred Mumford
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Re: incoherency solver

Post by Fred Mumford » Wed Aug 22, 2018 7:09 pm

Elliott Mellor wrote:
Wed Aug 22, 2018 3:05 pm
I've just checked and it actually seems you are now right, it does give more than one solution. However I am certain this never used to be the case.
Correct, the main thing that converted me to the crossword tools number solver was that the incoherency one only used to return a single solution. The incoherency one does have a couple of advantages though - unlimited free goes, and the ability to solve number problems that fall outside the Countdown rules.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Wed Aug 22, 2018 7:28 pm

Gavin Chipper wrote:
Wed Aug 22, 2018 6:02 pm
Vince Fernando wrote:
Wed Aug 22, 2018 2:18 pm
Gavin Chipper:
Elliott Mellor:

I am using the incoherency solver and it often gives more than one solution. My original question was whether the solution set is complete. If incoherency gives only one answer then my question is not a meaningful question in the first place.

Mathematics is never considered as subjective. If a different mathematician gets another solution then the initial axioms used by these two mathematicians are obviously different. If they use the same playing field then the results have to be identical.

5*100+10 is obviously different from 5*100+4+6 since there are 3 and 4 integers, respectively.
Then in this case they might be using different axioms, because by asking which numbers solutions in Countdown are identical, you're not formally defining it.
Pedantically, you are correct. However, one has to start with a reasonable set of axioms/definitions to study equivalence between solutions. Unfortunately, I do not believe that it is going to be an easy exercise.

Elliott Mellor
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Re: incoherency solver

Post by Elliott Mellor » Wed Aug 22, 2018 8:11 pm

Vince Fernando wrote:
Wed Aug 22, 2018 7:28 pm
Gavin Chipper wrote:
Wed Aug 22, 2018 6:02 pm
Vince Fernando wrote:
Wed Aug 22, 2018 2:18 pm
Gavin Chipper:
Elliott Mellor:

I am using the incoherency solver and it often gives more than one solution. My original question was whether the solution set is complete. If incoherency gives only one answer then my question is not a meaningful question in the first place.

Mathematics is never considered as subjective. If a different mathematician gets another solution then the initial axioms used by these two mathematicians are obviously different. If they use the same playing field then the results have to be identical.

5*100+10 is obviously different from 5*100+4+6 since there are 3 and 4 integers, respectively.
Then in this case they might be using different axioms, because by asking which numbers solutions in Countdown are identical, you're not formally defining it.
Pedantically, you are correct. However, one has to start with a reasonable set of axioms/definitions to study equivalence between solutions. Unfortunately, I do not believe that it is going to be an easy exercise.
Why do you want to know?

Gavin Chipper
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Re: incoherency solver

Post by Gavin Chipper » Wed Aug 22, 2018 9:04 pm

Vince Fernando wrote:
Wed Aug 22, 2018 7:28 pm
Gavin Chipper wrote:
Wed Aug 22, 2018 6:02 pm
Vince Fernando wrote:
Wed Aug 22, 2018 2:18 pm
Gavin Chipper:
Elliott Mellor:

I am using the incoherency solver and it often gives more than one solution. My original question was whether the solution set is complete. If incoherency gives only one answer then my question is not a meaningful question in the first place.

Mathematics is never considered as subjective. If a different mathematician gets another solution then the initial axioms used by these two mathematicians are obviously different. If they use the same playing field then the results have to be identical.

5*100+10 is obviously different from 5*100+4+6 since there are 3 and 4 integers, respectively.
Then in this case they might be using different axioms, because by asking which numbers solutions in Countdown are identical, you're not formally defining it.
Pedantically, you are correct. However, one has to start with a reasonable set of axioms/definitions to study equivalence between solutions. Unfortunately, I do not believe that it is going to be an easy exercise.
Which was my original point - the can of worms.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Thu Aug 23, 2018 6:21 pm

Gavin Chipper wrote:
Wed Aug 22, 2018 9:04 pm
Vince Fernando wrote:
Wed Aug 22, 2018 7:28 pm
Gavin Chipper wrote:
Wed Aug 22, 2018 6:02 pm

Then in this case they might be using different axioms, because by asking which numbers solutions in Countdown are identical, you're not formally defining it.
Pedantically, you are correct. However, one has to start with a reasonable set of axioms/definitions to study equivalence between solutions. Unfortunately, I do not believe that it is going to be an easy exercise.
Which was my original point - the can of worms.
I have some preliminary ideas how to solve the equivalence problem.

Vince Fernando
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Re: incoherency solver

Post by Vince Fernando » Thu Aug 23, 2018 6:24 pm

Elliott Mellor wrote:
Wed Aug 22, 2018 8:11 pm
Vince Fernando wrote:
Wed Aug 22, 2018 7:28 pm
Gavin Chipper wrote:
Wed Aug 22, 2018 6:02 pm

Then in this case they might be using different axioms, because by asking which numbers solutions in Countdown are identical, you're not formally defining it.
Pedantically, you are correct. However, one has to start with a reasonable set of axioms/definitions to study equivalence between solutions. Unfortunately, I do not believe that it is going to be an easy exercise.
Why do you want to know?
I do not understand your question.

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