### impossible number problems

Posted:

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

A group for contestants and lovers of the Channel 4 game show 'Countdown'.

http://www.c4countdown.co.uk/

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Posted: **Fri Jun 29, 2018 2:03 pm**

Is there a repository (data base) for 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/

Posted: **Fri Jun 29, 2018 4:35 pm**

We can also use incoherency.co.uk

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

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

(a) impossible problems (b) problems which are solvable but declared as impossible initially (c) problems with unconventional solutions

Posted: **Fri Jun 29, 2018 6:07 pm**

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.Vince Fernando wrote: ↑Fri Jun 29, 2018 5:51 pmThanks 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

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

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.

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.

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.

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...

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

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.

Posted: **Sat Jun 30, 2018 12:38 am**

The valid targets are between 101 and 999 inclusive, but that means there are 899 possible targets, not 898.Vince Fernando wrote: ↑Sat Jun 30, 2018 12:15 amSome 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.

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).

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.

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.

Posted: **Sat Jun 30, 2018 7:34 am**

Can I ask what sort of analysis you're looking to do? If you read the thread I linked, it should answer most or all of your questions.Vince Fernando wrote: ↑Fri Jun 29, 2018 11:42 pmA 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.

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.

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.

Posted: **Sat Jun 30, 2018 9:25 am**

Don't forget to multiply by 899....Vince Fernando wrote: ↑Sat Jun 30, 2018 8:45 amAs 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.

Again, read the thread I linked. And maybe how to spell my name properly.

FYI - the most likely to be solvable is 2 large and 4 small.

Posted: **Sun Jul 01, 2018 2:58 pm**

Elliott: My apologies for missing the last "t".

This number 13,243 is not too large. It may be possible to calculate the target range for each number set.

This number 13,243 is not too large. It may be possible to calculate the target range for each number set.