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### impossible number problems

Posted: Fri Jun 29, 2018 2:03 pm
Is there a repository (data base) for impossible number problems?

### Re: impossible number problems

Posted: Fri Jun 29, 2018 4:26 pm
Well, we always use this website if you want to check if numbers games are solvable: http://www.crosswordtools.com/numbers-game/

### Re: impossible number problems

Posted: Fri Jun 29, 2018 4:35 pm
We can also use incoherency.co.uk

### Re: impossible number problems

Posted: Fri Jun 29, 2018 4:36 pm
But to find the countdown solver thing it may be easier to just type into google countdown solver and then click on the one with incoherency.co.uk

### Re: impossible number problems

Posted: Fri Jun 29, 2018 5:51 pm
Thanks for links for solvers. I am interested in analysing
(a) impossible problems (b) problems which are solvable but declared as impossible initially (c) problems with unconventional solutions

### Re: impossible number problems

Posted: Fri Jun 29, 2018 6:07 pm
Vince Fernando wrote:
Fri Jun 29, 2018 5:51 pm
Thanks for links for solvers. I am interested in analysing
(a) impossible problems (b) problems which are solvable but declared as impossible initially (c) problems with unconventional solutions
There's such a large volume of numbers games (around 12 million it seems) that could happen that unless you have some sort of software/program to do it for you it's going to be an almost impossible task.

This thread may be relevant: viewtopic.php?f=3&t=11451&hilit=how+man ... s+games%3F

### Re: impossible number problems

Posted: Fri Jun 29, 2018 7:08 pm
That Dave Ricesky is a bit of an enigma. All his posts ever were within a month of each other.

### Re: impossible number problems

Posted: Fri Jun 29, 2018 11:42 pm
I accept that the number of possible problems is large but not too large.
for 6 small, 0 large = C(20,6) = 38,760
for 5 small, 1 large = C(20,5)*C(4,1) = 15,504*4 = 62,016
for 4 small, 2 large = C(20,4)*C(4,2) = 4,845*6 = 29,070
for 3 small, 3 large = C(20,3)*C(4,3) = 1,140*4 = 4560
for 2 small, 4 large = C(20,2) *C(4,4) = 190
total = 134,596
where C denotes combinations.
There are 898 targets (from 101 to 999) and so there are 134,596*898 = 120,867,208 problems if the target is also included. However, the targets do not have to explicitly stored if all possible problems are going to be recorded.

A small sample fraction of then solvable and unsolvable problems can be used to study the number problem. It is possible to do (Monte Carlo) simulations
without storing much data but the program which classifies the solvable and non-solvable problems has to be 100% accurate. Web based programs are not useful for this purpose.

### Re: impossible number problems

Posted: Sat Jun 30, 2018 12:07 am
Are there not 899 targets? Shouldn't that be 121,001,804 possible numbers games then?

Now someone merely just has to memorise all of them...

### Re: impossible number problems

Posted: Sat Jun 30, 2018 12:15 am
Some believe that 100 is not a valid target since if the number 100 is in the rack and the target is also 100 then there is no computations to be done. Using this assumption (many believe that this is the case with C4 countdown) there are only 898 targets.

### Re: impossible number problems

Posted: Sat Jun 30, 2018 12:38 am
Vince Fernando wrote:
Sat Jun 30, 2018 12:15 am
Some believe that 100 is not a valid target since if the number 100 is in the rack and the target is also 100 then there is no computations to be done. Using this assumption (many believe that this is the case with C4 countdown) there are only 898 targets.
The valid targets are between 101 and 999 inclusive, but that means there are 899 possible targets, not 898.

### Re: impossible number problems

Posted: Sat Jun 30, 2018 1:32 am
Sorry for the mistake; as Graeme Cole and Rhys Benjamin have indicated as indicated, there are 899 targets (not 898).

### Re: impossible number problems

Posted: Sat Jun 30, 2018 3:51 am
Vince, you have greatly overstated the number of possible problems - you seem to be treating the 20 small tiles as if they are all different, which is not the case.

Take the easiest case, 4 large - how can there possibly be 190 combinations? The large numbers never change, and even a simple 10 x 10 calculation only gives 100. Of those 100, 90 of them are double counted (eg 2,8 is the same as 8,2) so we are left with just 55.

### Re: impossible number problems

Posted: Sat Jun 30, 2018 7:34 am
Vince Fernando wrote:
Fri Jun 29, 2018 11:42 pm
A small sample fraction of then solvable and unsolvable problems can be used to study the number problem. It is possible to do (Monte Carlo) simulations
without storing much data but the program which classifies the solvable and non-solvable problems has to be 100% accurate. Web based programs are not useful for this purpose.

### Re: impossible number problems

Posted: Sat Jun 30, 2018 8:45 am
As Elliot Mellor has pointed out, my values were gross over estimates. The correct results appear to be
for 6 small, 0 large = 2850
for 5 small, 1 large = 1452*4 = 5808
for 4 small, 2 large = 615*6 = 3690
for 3 small, 3 large = 210*4 = 840
for 2 small, 4 large = 55*1 = 55
total = 13243
This number is not too large for analysis of the number problem. Is it possible to classify the problems to bring out difficult and impossible problems? As an example, if there is an "1" then it is not active for multiplication and division. If there are two '1's then the problem becomes more difficult to solve since we loose 4 operations. Duplicated values iii genera, (e.g. two '4's) will also make the problem more difficult. Such a situation is more probable with 5 small numbers.

### Re: impossible number problems

Posted: Sat Jun 30, 2018 9:25 am
Vince Fernando wrote:
Sat Jun 30, 2018 8:45 am
As Elliot Mellor has pointed out, my values were gross over estimates. The correct results appear to be
for 6 small, 0 large = 2850
for 5 small, 1 large = 1452*4 = 5808
for 4 small, 2 large = 615*6 = 3690
for 3 small, 3 large = 210*4 = 840
for 2 small, 4 large = 55*1 = 55
total = 13243
This number is not too large for analysis of the number problem. Is it possible to classify the problems to bring out difficult and impossible problems? As an example, if there is an "1" then it is not active for multiplication and division. If there are two '1's then the problem becomes more difficult to solve since we loose 4 operations. Duplicated values iii genera, (e.g. two '4's) will also make the problem more difficult. Such a situation is more probable with 5 small numbers.
Don't forget to multiply by 899....