incoherency solver
Posted: Wed Aug 15, 2018 8:26 pm
Does the incoherency number solver give all possible solutions?
Yep.Vince Fernando wrote: ↑Wed Aug 15, 2018 8:26 pm Does the incoherency number solver give all possible solutions?
A group for contestants and lovers of the Channel 4 game show 'Countdown'.
http://c4countdown.co.uk/
Yep.Vince Fernando wrote: ↑Wed Aug 15, 2018 8:26 pm Does the incoherency number solver give all possible solutions?
I've used it a lot to practise for the show. It gives all possible solutions.Vince Fernando wrote: ↑Sat Aug 18, 2018 11:40 am Owen Carroll:
Do you have any evidence to back your claim?
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.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.
I think you're opening a whole can of worms talking about what counts as equivalent solutions though.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?
More than 1. It will only ever give 1 solution regardless of whether there is 2 solutions or 200 solutions.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"?
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.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.
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.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.
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.Gavin Chipper wrote: ↑Wed Aug 22, 2018 12:14 pmMaybe 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.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.
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.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.
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.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.
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.Gavin Chipper wrote: ↑Wed Aug 22, 2018 6:02 pmThen 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.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.
Why do you want to know?Vince Fernando wrote: ↑Wed Aug 22, 2018 7:28 pmPedantically, 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.Gavin Chipper wrote: ↑Wed Aug 22, 2018 6:02 pmThen 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.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.
Which was my original point - the can of worms.Vince Fernando wrote: ↑Wed Aug 22, 2018 7:28 pmPedantically, 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.Gavin Chipper wrote: ↑Wed Aug 22, 2018 6:02 pmThen 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.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.
I have some preliminary ideas how to solve the equivalence problem.Gavin Chipper wrote: ↑Wed Aug 22, 2018 9:04 pmWhich was my original point - the can of worms.Vince Fernando wrote: ↑Wed Aug 22, 2018 7:28 pmPedantically, 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.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.
I do not understand your question.Elliott Mellor wrote: ↑Wed Aug 22, 2018 8:11 pmWhy do you want to know?Vince Fernando wrote: ↑Wed Aug 22, 2018 7:28 pmPedantically, 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.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.