How many Numbers puzzles are there in total?
 Peter Clarke
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How many Numbers puzzles are there in total?
Is there a way you can work out the amount of countdown numbers games? I know there are 24 numbers to pick from (two each of numbers 110 and 25, 50, 75, 100) and I think you work out the amount of numbers combinations (which is the part I don't know how to do) and then multiply by the amount of targets which is 898 I think (999101=899 ).
Does anyone know how to work out the amount of possible numbers combinations? I know there are 24 numbers and 6 numbers in a game obviously. It wouldn't be 999,999 surely because those are just the numbers 09 (10 numbers) and there are six of one number each (filling all gaps). In this case, there are two of numbers 110 each and 25, 50, 75, 100.
Hope you all get what I mean, apologies if I haven't been clear.
Does anyone know how to work out the amount of possible numbers combinations? I know there are 24 numbers and 6 numbers in a game obviously. It wouldn't be 999,999 surely because those are just the numbers 09 (10 numbers) and there are six of one number each (filling all gaps). In this case, there are two of numbers 110 each and 25, 50, 75, 100.
Hope you all get what I mean, apologies if I haven't been clear.
Re: How many Numbers puzzles are there in total?
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Last edited by Conor on Wed Jan 06, 2016 11:29 pm, edited 1 time in total.

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Re: How many Numbers puzzles are there in total?
There are 2850 possible 6 smalls, 5808 of 1 large, 3690 of 2 large, 840 of 3 large and 55 of 4 large, so 13243 different selections in total.
As to how to work it out, it's all about factorials. For example, the number of 6 small is 10!/(6!4!) plus 10!/(5!5!) x 5!/(1!4!) plus 10!/(4!6!) x 4!/(2!2!) plus 10!/(3!7!). And it really is as simple as that.
As to how to work it out, it's all about factorials. For example, the number of 6 small is 10!/(6!4!) plus 10!/(5!5!) x 5!/(1!4!) plus 10!/(4!6!) x 4!/(2!2!) plus 10!/(3!7!). And it really is as simple as that.
Re: How many Numbers puzzles are there in total?
There's four per episode.
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Re: How many Numbers puzzles are there in total?
Right. I'm probably gonna make about a hundred arithmetic errors and someone will answer as I type this as it's been up for over an hour but let's have a crack.
As you say, there's 899 targets so just multiply the amount of selections by 899 to get your answer.
I'd go about it by splitting the selection into the different types.
With 4L, the only thing that can change are the two smalls (assuming when the numbers are the same but in a different order it counts as the same puzzle. If not, then do some shit with factorials). There are 55 different small selections you can get (and thus only 55 different 4L selections, so hardcore 4Lers could literally learn all targets available with each of the 55). This is because there's 10x10=100 ways to pick two small. Ten are going to be the same number twice, and the other 90 are going to all have the reverse in it (so 2, 3 and 3, 2 are both given). You can thus get rid of half the 90, making 10+45=55. I use that idea for the rest of them.
OK, so 55 4L selections. Moving onto 3L. There's four different ways of doing the larges, cause each one will be missing one of the four larges. With the smalls, you have 3 smalls which can either be two of the same and another one, or three different ones. (Thanks god I'm not working out the chance of each cause that'd be a right ballache.) The first scenario is 90 combinations as it's like the thing I did earlier except you can't have two (three) of the same cause there's only 2 of each number, and you can't get rid of half as 2, 2, 3 is different to 3, 3, 2. The second scenario is just 10 choose 3 = 10!/(3!*7!) =120. Adding them gives 210 ways of doing 3 smalls, multiplied by 4 for the larges, gives 840 different possible 3L selections.
2L time. There's 6 ways of doing the larges (25 50 , 25 75 , 25 100 , 50 75 , 50 100 , 75 100). The smalls can either be:
4 different ones (10 choose 4 = 210)
Two pairs (just 10x9/2=45 (10 choose 2) using stuff from earlier, and 2233 is the same as 3322 but 1111 can't exist)
One pair and two different ones. Ten different options for the pair and then 9 choose 2 for the other two = 10*36=360. That gives you 360+210+45=615 ways of doing 4 smalls, times 6 which gives you 3690 different 2L selections.
Gee I've probably made a really stupid maths error somewhere
1L There's obviously 4 different ways of doing the larges. Smalls:
Two pairs one singlet (10c2 times 8c1 =45*8=360)
One pair three singles (10c1 times 9c3 =10*84=840)
Five singletons (10c5=252)
Adding them gives 360+840+252=1452 ways of 5 smalling times 4 is 5808 1L selections
Six small. This selection should be illegal but it isn't so
Three pairs = (10c3=120)
Two pair two single = (10c2*8c2=45*28=1260)
One pair four single = (10c1*9c4=10*126=1260 again, spooky)
Six single = (10c6=210)
Add them = 2850 six small selections. All of them suck.
I probably mathsed everything wrong
Add them all is 55+840+3690+5808+2850= 13,243 numbers selections.
Times the targets and you have 13,243*899= 11,905,457 of whatever I was working out.
Now to look over all the mistakes I've made
Edit: Fuck's sake Fred
As you say, there's 899 targets so just multiply the amount of selections by 899 to get your answer.
I'd go about it by splitting the selection into the different types.
With 4L, the only thing that can change are the two smalls (assuming when the numbers are the same but in a different order it counts as the same puzzle. If not, then do some shit with factorials). There are 55 different small selections you can get (and thus only 55 different 4L selections, so hardcore 4Lers could literally learn all targets available with each of the 55). This is because there's 10x10=100 ways to pick two small. Ten are going to be the same number twice, and the other 90 are going to all have the reverse in it (so 2, 3 and 3, 2 are both given). You can thus get rid of half the 90, making 10+45=55. I use that idea for the rest of them.
OK, so 55 4L selections. Moving onto 3L. There's four different ways of doing the larges, cause each one will be missing one of the four larges. With the smalls, you have 3 smalls which can either be two of the same and another one, or three different ones. (Thanks god I'm not working out the chance of each cause that'd be a right ballache.) The first scenario is 90 combinations as it's like the thing I did earlier except you can't have two (three) of the same cause there's only 2 of each number, and you can't get rid of half as 2, 2, 3 is different to 3, 3, 2. The second scenario is just 10 choose 3 = 10!/(3!*7!) =120. Adding them gives 210 ways of doing 3 smalls, multiplied by 4 for the larges, gives 840 different possible 3L selections.
2L time. There's 6 ways of doing the larges (25 50 , 25 75 , 25 100 , 50 75 , 50 100 , 75 100). The smalls can either be:
4 different ones (10 choose 4 = 210)
Two pairs (just 10x9/2=45 (10 choose 2) using stuff from earlier, and 2233 is the same as 3322 but 1111 can't exist)
One pair and two different ones. Ten different options for the pair and then 9 choose 2 for the other two = 10*36=360. That gives you 360+210+45=615 ways of doing 4 smalls, times 6 which gives you 3690 different 2L selections.
Gee I've probably made a really stupid maths error somewhere
1L There's obviously 4 different ways of doing the larges. Smalls:
Two pairs one singlet (10c2 times 8c1 =45*8=360)
One pair three singles (10c1 times 9c3 =10*84=840)
Five singletons (10c5=252)
Adding them gives 360+840+252=1452 ways of 5 smalling times 4 is 5808 1L selections
Six small. This selection should be illegal but it isn't so
Three pairs = (10c3=120)
Two pair two single = (10c2*8c2=45*28=1260)
One pair four single = (10c1*9c4=10*126=1260 again, spooky)
Six single = (10c6=210)
Add them = 2850 six small selections. All of them suck.
I probably mathsed everything wrong
Add them all is 55+840+3690+5808+2850= 13,243 numbers selections.
Times the targets and you have 13,243*899= 11,905,457 of whatever I was working out.
Now to look over all the mistakes I've made
Edit: Fuck's sake Fred
cheers maus

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Re: How many Numbers puzzles are there in total?
Is that the wrong way round?Peter Clarke wrote:and then multiply by the amount of targets which is 898 I think (999101=899 ).

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Re: How many Numbers puzzles are there in total?
Ah yes, the Bernard Cribbins follow up single that got banned.Thomas Carey wrote:Fuck's sake Fred
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Re: How many Numbers puzzles are there in total?
Oh yeah there are 899 targets, so 999100=899. Silly me haha.
That must be right considering you both got the same answer with different methods. Thanks both Fred and Thomas!
How long did it take you to do that Thomas haha?
That must be right considering you both got the same answer with different methods. Thanks both Fred and Thomas!
How long did it take you to do that Thomas haha?
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Re: How many Numbers puzzles are there in total?
Like 10 minutes including typing the thing. I did what Fred did but just explained it better, hopefully you can follow it
cheers maus

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Re: How many Numbers puzzles are there in total?
I don't believe you could do all that including typing in 10 minutes!Thomas Carey wrote:Like 10 minutes including typing the thing. I did what Fred did but just explained it better, hopefully you can follow it
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Re: How many Numbers puzzles are there in total?
Yeah probably like 20 who careGavin Chipper wrote:I don't believe you could do all that including typing in 10 minutes!Thomas Carey wrote:Like 10 minutes including typing the thing. I did what Fred did but just explained it better, hopefully you can follow it
cheers maus

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Re: How many Numbers puzzles are there in total?
No, just this one, and quite a bad one as well.Thomas Carey wrote:Right. I'm probably gonna make about a hundred arithmetic errors
Seeing as I'm too thick to understand Fred's method and probably won't live long enough to read through Tom's, I'll present my own alternative method. Instead of going through each of the numbers types individually, I'm going to look at it in terms of how many pairs of repeated numbers there are. There can be 0, 1, 2 or 3 in a numbers game.
0 repeated numbers: I'm not making any distinction between large and small, so there are 14c6 (14 choose 6) combinations with no repeated numbers, which equals 3,003. I'll save the multiplication by 899 until the end to make things easier.
1 repeated number: 10 possibilities for the repeated number, multiplied by 13c4 for the rest, so 10 x 715 = 7,150.
2 repeated numbers: 10c2 ways for determining which two numbers are repeated, multiplied by 12c2 for the rest, giving 45 x 66 = 2,970.
Finally, for 3 repeated numbers, there are simply 10c3 possibilities, which equals 120.
Adding up all of these numbers again gives 13,243 and multiply by 899 and you have 11,905,457.
Re: How many Numbers puzzles are there in total?
Fred Mumford wrote:Ah yes, the Bernard Cribbins follow up single that got banned.Thomas Carey wrote:Fuck's sake Fred
Re: How many Numbers puzzles are there in total?
Can we now have a breakdown of those 11,905,457 games please?
I'd like to know how many games are possible to solve, how many 1 away is the best, 2 away, and so on.
Would probably be neat to split this out by selection type as well.
Thanks in advance, will check back in ten minutes.
Actually, I'd also be interested to see it split out by target. So some kind of threedimensional reporting cube please. 15 minutes.
I'd like to know how many games are possible to solve, how many 1 away is the best, 2 away, and so on.
Would probably be neat to split this out by selection type as well.
Thanks in advance, will check back in ten minutes.
Actually, I'd also be interested to see it split out by target. So some kind of threedimensional reporting cube please. 15 minutes.
Re: How many Numbers puzzles are there in total?
I'm actually going to do this ^ myself. I'll publish my results. Then numbers games can be reduced to a simple memory exercise. Ocelots seem nice despite shin camera, and all that.

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Re: How many Numbers puzzles are there in total?
Gavin Chipper wrote:I don't believe you could do all that including typing in 10 minutes!Thomas Carey wrote:Like 10 minutes including typing the thing. I did what Fred did but just explained it better, hopefully you can follow it
I can believe that this was completed inside 10 minutes by the way.Conor wrote:.
Re: How many Numbers puzzles are there in total?
Fuck. Even with a well optimized solver this is gonna take a LOOONG time to accumulate all the data. Somebody else must have already done this, surely?!Jon Corby wrote:I'm actually going to do this ^ myself. I'll publish my results. Then numbers games can be reduced to a simple memory exercise. Ocelots seem nice despite shin camera, and all that.
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Re: How many Numbers puzzles are there in total?
Didn't William TungstenPaedo do it? It's on another hard drive, but I've definitely got emails from him from about 2002 where we were discussing (arguing) whether 100 was a legitimate target if there was a 100 in the selection, something like that. If his website's still online, I'd look there first.Jon Corby wrote:Fuck. Even with a well optimized solver this is gonna take a LOOONG time to accumulate all the data. Somebody else must have already done this, surely?!Jon Corby wrote:I'm actually going to do this ^ myself. I'll publish my results. Then numbers games can be reduced to a simple memory exercise. Ocelots seem nice despite shin camera, and all that.
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Re: How many Numbers puzzles are there in total?
But what about when 6s and 9s can come out upside down like Ms and Ws do? That must change the numbers available
Re: How many Numbers puzzles are there in total?
Wanna link me up? I don't fancy searching for somebody called Peado while I'm at work...JimBentley wrote:Didn't William TungstenPaedo do it? It's on another hard drive, but I've definitely got emails from him from about 2002 where we were discussing (arguing) whether 100 was a legitimate target if there was a 100 in the selection, something like that. If his website's still online, I'd look there first.Jon Corby wrote:Fuck. Even with a well optimized solver this is gonna take a LOOONG time to accumulate all the data. Somebody else must have already done this, surely?!Jon Corby wrote:I'm actually going to do this ^ myself. I'll publish my results. Then numbers games can be reduced to a simple memory exercise. Ocelots seem nice despite shin camera, and all that.
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Re: How many Numbers puzzles are there in total?
I may have intentionally misremembered his name for comedy value. Anyway, here you go:Jon Corby wrote:Wanna link me up? I don't fancy searching for somebody called Peado while I'm at work...JimBentley wrote:Didn't William TungstenPaedo do it? It's on another hard drive, but I've definitely got emails from him from about 2002 where we were discussing (arguing) whether 100 was a legitimate target if there was a 100 in the selection, something like that. If his website's still online, I'd look there first.
http://www.crosswordtools.com/numbersgame/faq.php
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Re: How many Numbers puzzles are there in total?
That doesn't give me what I'm after at all. I want a definitive list for ALL numbers games. They've done a sample using random games. And even then they've just listed how many were solvable, how many were one away. I want EVERYTHING.JimBentley wrote:I may have intentionally misremembered his name for comedy value. Anyway, here you go:Jon Corby wrote:Wanna link me up? I don't fancy searching for somebody called Peado while I'm at work...JimBentley wrote:Didn't William TungstenPaedo do it? It's on another hard drive, but I've definitely got emails from him from about 2002 where we were discussing (arguing) whether 100 was a legitimate target if there was a 100 in the selection, something like that. If his website's still online, I'd look there first.
http://www.crosswordtools.com/numbersgame/faq.php
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Re: How many Numbers puzzles are there in total?
Hey, I never said there would be anything of value there, I think the guy's a bit of a dick anyway.Jon Corby wrote:That doesn't give me what I'm after at all. I want a definitive list for ALL numbers games. They've done a sample using random games. And even then they've just listed how many were solvable, how many were one away. I want EVERYTHING.
I'm sure someone's done this thoroughly, though, I just can't quite remember who.
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Re: How many Numbers puzzles are there in total?
I was also wondering how we find out how many of those games are possible or not. Good chart there posted!!
I also wonder how RR figures out whether a Numbers game is impossible, or does she just get told that?
I also wonder how RR figures out whether a Numbers game is impossible, or does she just get told that?

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Re: How many Numbers puzzles are there in total?
My understanding is that she gets told whether or not it's possible, in order to save her from trying to work out an impossible numbers game, but never how to do it.Peter Clarke wrote:I was also wondering how we find out how many of those games are possible or not. Good chart there posted!!
I also wonder how RR figures out whether a Numbers game is impossible, or does she just get told that?
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Re: How many Numbers puzzles are there in total?
That's interesting. I was wondering if she got told whether it was possible after watching an episode this week where she said she got three away when the nearest possible was two away. This doesn't count as a spoiler right? I tried to match it with the background colour just in case lol (highlight it to read it).Jack Worsley wrote:My understanding is that she gets told whether or not it's possible, in order to save her from trying to work out an impossible numbers game, but never how to do it.Peter Clarke wrote:I was also wondering how we find out how many of those games are possible or not. Good chart there posted!!
I also wonder how RR figures out whether a Numbers game is impossible, or does she just get told that?
I know CV had the numbers written down on her clipboard for her so she doesn't waste 10 seconds of the time writing them down, I assume RR does too.
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Re: How many Numbers puzzles are there in total?
Yes. Sometimes you can see Rachel using the clipboard if it's a difficult round.Peter Clarke wrote:That's interesting. I was wondering if she got told whether it was possible after watching an episode this week where she said she got three away when the nearest possible was two away. This doesn't count as a spoiler right? I tried to match it with the background colour just in case lol (highlight it to read it).Jack Worsley wrote:My understanding is that she gets told whether or not it's possible, in order to save her from trying to work out an impossible numbers game, but never how to do it.Peter Clarke wrote:I was also wondering how we find out how many of those games are possible or not. Good chart there posted!!
I also wonder how RR figures out whether a Numbers game is impossible, or does she just get told that?
I know CV had the numbers written down on her clipboard for her so she doesn't waste 10 seconds of the time writing them down, I assume RR does too.

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Re: How many Numbers puzzles are there in total?
From RRs reactions to the crew sometimes it looks like she is probably told easy ones are possible sometimes!
Re: How many Numbers puzzles are there in total?
My hunch is that she isn't told until after the 30 seconds. My thought process changes a lot if I have the luxury of aiming solely for the target rather than trying to get as nearaspossible (and she'll often say that she was n away).Philip Wilson wrote:From RRs reactions to the crew sometimes it looks like she is probably told easy ones are possible sometimes!
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Re: How many Numbers puzzles are there in total?
I've modified my crappy numbers solver to work this out. It's going to take roughly until May 25th until my laptop finishes it, though, and I'm not sure it'll last that long. But it's worth a shot.JimBentley wrote:Hey, I never said there would be anything of value there, I think the guy's a bit of a dick anyway.Jon Corby wrote:That doesn't give me what I'm after at all. I want a definitive list for ALL numbers games. They've done a sample using random games. And even then they've just listed how many were solvable, how many were one away. I want EVERYTHING.
I'm sure someone's done this thoroughly, though, I just can't quite remember who.
Do you want to know which ones are solvable, one away etc or just how many?
cheers maus
Re: How many Numbers puzzles are there in total?
Don't worry Tom, I'm already on it. My estimated completion time is well under yours though (about a month running on my desktop!) I'm producing a csv file of basically every numbers game so I can slice it all up at will. My solver program can take parameters (e.g. produce the csv for games 10,000,000  11,905,457) so I might share out the CPU work if there are some volunteers...Thomas Carey wrote:I've modified my crappy numbers solver to work this out. It's going to take roughly until May 25th until my laptop finishes it, though, and I'm not sure it'll last that long. But it's worth a shot.JimBentley wrote:Hey, I never said there would be anything of value there, I think the guy's a bit of a dick anyway.Jon Corby wrote:That doesn't give me what I'm after at all. I want a definitive list for ALL numbers games. They've done a sample using random games. And even then they've just listed how many were solvable, how many were one away. I want EVERYTHING.
I'm sure someone's done this thoroughly, though, I just can't quite remember who.
Do you want to know which ones are solvable, one away etc or just how many?
Also, who is this (on the left) from the solver page that Jim linked to:
?
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Re: How many Numbers puzzles are there in total?
I think she was called something like Ariane or something, she was a standup comic and a staunch atheist. She was lovely. I can't remember any more than that but Chris Philpot (if he still reads) will be able to tell you more.Jon Corby wrote:Also, who is this (on the left) from the solver page that Jim linked to:
?
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Re: How many Numbers puzzles are there in total?
Is that Philpot in the picture as well?JimBentley wrote:I think she was called something like Ariane or something, she was a standup comic and a staunch atheist. She was lovely. I can't remember any more than that but Chris Philpot (if he still reads) will be able to tell you more.Jon Corby wrote:Also, who is this (on the left) from the solver page that Jim linked to:
?
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Re: How many Numbers puzzles are there in total?
Pretty sure so, he posted quite a bit at the time about it.Jon Corby wrote:Is that Philpot in the picture as well?JimBentley wrote:I think she was called something like Ariane or something, she was a standup comic and a staunch atheist. She was lovely. I can't remember any more than that but Chris Philpot (if he still reads) will be able to tell you more.Jon Corby wrote:Also, who is this (on the left) from the solver page that Jim linked to:
?
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Re: How many Numbers puzzles are there in total?
I think she was something to do with the "God is probably not on this bus, so don't bother running for it" campaign.
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Re: How many Numbers puzzles are there in total?
http://wiki.apterous.org/Ariane_Sherine . There's quite a lot of results from ages ago if you search her on this forum.
http://wiki.apterous.org/Chris_Philpot Also, says on Chris' thing that they had a rematch and that she actually gave Chris her teapot.
http://wiki.apterous.org/Chris_Philpot Also, says on Chris' thing that they had a rematch and that she actually gave Chris her teapot.
cheers maus
Re: How many Numbers puzzles are there in total?
I made a (what turned out to be huge) optimization to my procedure and it's now finished. Yes, I have a list of all 11,905,457 numbers games, and whether they're possible or not (and if not, how close you can get). My optimization was actually simply to ignore the method itself  I was writing out a 'method' for each game, which I decided was pointless since there's nothing really you can sensibly do with them as a set. If you want a method for a particular game you can bung it through a solver in a second. (The reason that this sped it up so much was because solutions have to be optimized  my program bruteforced EVERY combination of operations with the numbers. In order to get a sensible method, you find the one with the fewest steps, otherwise it might go 25*5 = 125, 3+4 = 7, 100+6 = 106 to solve the puzzle with a target of 106. Obviously the first few steps are garbage, but the solver doesn't know that without adding expensive overheads. If we don't care what the method is, we can drop out as soon as we hit any method that gets the right solution. Since most games are possible to solve exactly, this makes a huge saving.Jon Corby wrote:Don't worry Tom, I'm already on it. My estimated completion time is well under yours though (about a month running on my desktop!) I'm producing a csv file of basically every numbers game so I can slice it all up at will. My solver program can take parameters (e.g. produce the csv for games 10,000,000  11,905,457) so I might share out the CPU work if there are some volunteers...
So, maybe I should just turn the file over to Graeme so he can start answering questions. Or maybe I'd like a little play around with it first.
Any specific questions once we get past the ones posed above? Do you think, for example, there is a selection of numbers for which you can always get 10 points, regardless of the target?

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Re: How many Numbers puzzles are there in total?
This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.Jon Corby wrote:Do you think, for example, there is a selection of numbers for which you can always get 10 points, regardless of the target?
Re: How many Numbers puzzles are there in total?
Fuck you, this is supposed to be the kind of groundbreaking stuff that this dataset allows us to know. Well if there's one, there's probably others. And I'll know them, and you won't.Gavin Chipper wrote:This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.Jon Corby wrote:Do you think, for example, there is a selection of numbers for which you can always get 10 points, regardless of the target?
Re: How many Numbers puzzles are there in total?
That is just one of 1,226 selections which can be maxed with every possible target from 101999.Gavin Chipper wrote:This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.Jon Corby wrote:Do you think, for example, there is a selection of numbers for which you can always get 10 points, regardless of the target?
614 of these are 1 large selections.
603 are 2 large.
4 are 3 large.
5 are 6 small.
THIS IS A GOLDMINE OF INTERESTING INFORMATION.

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Re: How many Numbers puzzles are there in total?
I'll guess that 9, 4, 5, 2, 3, 8 is one of the 6 smalls?Jon Corby wrote:That is just one of 1,226 selections which can be maxed with every possible target from 101999.Gavin Chipper wrote:This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.Jon Corby wrote:Do you think, for example, there is a selection of numbers for which you can always get 10 points, regardless of the target?
614 of these are 1 large selections.
603 are 2 large.
4 are 3 large.
5 are 6 small.
THIS IS A GOLDMINE OF INTERESTING INFORMATION.
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Re: How many Numbers puzzles are there in total?
What about the same question the other way round... which targets are solvable by every 1large selection? Every 2 large? 3 large? 4 large?
Which target is solvable by the fewest selections?
Which target is solvable by the fewest selections?

 Postapocalypse
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Re: How many Numbers puzzles are there in total?
You're not allowed to ask questions!Graeme Cole wrote:What about the same question the other way round... which targets are solvable by every 1large selection? Every 2 large? 3 large? 4 large?
Which target is solvable by the fewest selections?

 Series 72 Champion
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Re: How many Numbers puzzles are there in total?
I'll guess 911 or 937 for the least solvable target. High primes, and good distance from multiples of 25 (I don't think the 937.5 trick will add that many for the second).Graeme Cole wrote:What about the same question the other way round... which targets are solvable by every 1large selection? Every 2 large? 3 large? 4 large?
Which target is solvable by the fewest selections?
 JimBentley
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Re: How many Numbers puzzles are there in total?
I'll guess that they all have to involve a 10, so more like  and this is just off the top of my head, you understand  (2, 5, 7, 8, 9, 10), (3, 4, 7, 8, 9, 10), (5, 6, 7, 8, 9, 10), (6, 7, 8, 8, 9, 10) and (6, 7, 8, 9, 10, 10).Dan McColm wrote:I'll guess that 9, 4, 5, 2, 3, 8 is one of the 6 smalls?Jon Corby wrote:That is just one of 1,226 selections which can be maxed with every possible target from 101999...
5 are 6 small.
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Re: How many Numbers puzzles are there in total?
Fuck you Jim, don't you be stealing my thunder now!
Have you done the same work?
(Jim is entirely correct with those five sets of six small, in case it wasn't obvious.)
Have you done the same work?
(Jim is entirely correct with those five sets of six small, in case it wasn't obvious.)
Re: How many Numbers puzzles are there in total?
Here is the breakdown by type, and how far away you can get:
Code: Select all
Zero away 1 away 2 away 3 away 4 away 5 away 6 away 7 away 8 away 9 away 10 away 11+ away
6S 1963726 (76.64%) 353472 65417 26954 15232 9859 7357 5780 4589 3945 3326 102493
1L 4966076 (95.11%) 220295 21730 5813 2527 1272 713 470 339 264 217 1676
2L 3192103 (96.23%) 112258 8487 1880 865 435 313 207 144 114 78 426
3L 693131 (91.79%) 53875 4577 1332 724 461 296 206 139 87 64 268
4L 43710 (88.40%) 4661 556 179 112 75 42 28 22 18 16 26
 JimBentley
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Re: How many Numbers puzzles are there in total?
Haha no, but I once asked one of my friends (sadly dead now I'm afraid) to do something similar and have finally dug out the results from an ancient hard drive. Incidentally he only made it 10,871,986 possible games, so it's possible he missed some or did something wrong somewhere (I've only got the text output, rather than the code, so I can't really tell).Jon Corby wrote:Fuck you Jim, don't you be stealing my thunder now!
Have you done the same work?
(Jim is entirely correct with those five sets of six small, in case it wasn't obvious.)
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Re: How many Numbers puzzles are there in total?
1 Large: 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 119, 120, 125, 136, 150, 200, 210, 216, 300, 450Graeme Cole wrote:What about the same question the other way round... which targets are solvable by every 1large selection? Every 2 large? 3 large? 4 large?
2 Large: 101, 102, 104, 105, 106, 111, 114, 119, 124, 125, 126, 134, 144, 145, 146, 149, 150, 151, 175, 199, 200, 250, 300, 350, 400, 450, 500, 550, 600, 625, 650, 700, 750, 800, 900
3 Large: 101, 102, 103, 104, 105, 106, 108, 111, 112, 124, 125, 126, 127, 129, 136, 139, 142, 144, 148, 149, 150, 151, 152, 156, 174, 175, 176, 199, 200, 201, 224, 225, 226, 250, 275, 276, 300, 325, 350, 375, 400, 425, 450, 475, 500, 525, 550, 575, 600, 625, 650, 675, 700, 750, 825, 900
4 Large : 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 160, 162, 167, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 210, 211, 222, 223, 225, 226, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258, 267, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 292, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 308, 310, 322, 324, 325, 326, 328, 336, 342, 344, 346, 347, 348, 350, 352, 353, 354, 356, 357, 364, 372, 375, 376, 378, 396, 397, 399, 400, 403, 404, 406, 425, 446, 450, 453, 454, 456, 475, 492, 496, 500, 504, 525, 550, 575, 600, 624, 625, 650, 675, 700, 725, 750, 775, 800, 825, 850, 900, 925, 938, 950, 975
Re: How many Numbers puzzles are there in total?
947, but even then there 9,017 selections which solve and only 4,226 which do not.Graeme Cole wrote:Which target is solvable by the fewest selections?
It's then small steps to the next worst, 941 (9045 solve, 4,198 don't), and similarly onto 967, 933 and 937 (TCap's other guess of 911 is #23 in the list.)
The first 'baddun' that isn't in the 900s is 853 at rank #13 (9453 solve, 3790 don't)
Re: How many Numbers puzzles are there in total?
This selection has 41 unsolvable targets:Dan McColm wrote:I'll guess that 9, 4, 5, 2, 3, 8 is one of the 6 smalls?Jon Corby wrote: That is just one of 1,226 selections which can be maxed with every possible target from 101999.
614 of these are 1 large selections.
603 are 2 large.
4 are 3 large.
5 are 6 small.
THIS IS A GOLDMINE OF INTERESTING INFORMATION.
607, 631, 641, 655, 761, 769, 771, 785, 799, 803, 823, 827, 829, 839, 878, 901, 905, 914, 919, 921, 929, 934, 937, 943, 947, 949, 953, 955, 957, 959, 961, 965, 967, 971, 977, 979, 983, 985, 989, 991, 995
(You can get one away on each of these btw.)
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Re: How many Numbers puzzles are there in total?
961 is also a significant number and I will give a prize of one new penny for the first person (who isn't Jon) to say why.
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Re: How many Numbers puzzles are there in total?
I hope his death wasn't related to this pursuit in any way, maybe somebody is trying to keep this information under wraps? I'll be extra vigilant on my way home tonight.JimBentley wrote:Haha no, but I once asked one of my friends (sadly dead now I'm afraid) to do something similar and have finally dug out the results from an ancient hard drive. Incidentally he only made it 10,871,986 possible games, so it's possible he missed some or did something wrong somewhere (I've only got the text output, rather than the code, so I can't really tell).
Re: How many Numbers puzzles are there in total?
I have no fucking idea what is significant about 961 by the way, if that helps anyone.JimBentley wrote:961 is also a significant number and I will give a prize of one new penny for the first person (who isn't Jon) to say why.
Re: How many Numbers puzzles are there in total?
Interestingly, the percentage solvable on that Solver FAQ are less accurate than I would have expected. I wonder how big their sample size was? Or if they've made some kind of error? Because I sure as hell haven'tJon Corby wrote:Here is the breakdown by type, and how far away you can get:
Code: Select all
Zero away 1 away 2 away 3 away 4 away 5 away 6 away 7 away 8 away 9 away 10 away 11+ away 6S 1963726 (76.64%) 353472 65417 26954 15232 9859 7357 5780 4589 3945 3326 102493 1L 4966076 (95.11%) 220295 21730 5813 2527 1272 713 470 339 264 217 1676 2L 3192103 (96.23%) 112258 8487 1880 865 435 313 207 144 114 78 426 3L 693131 (91.79%) 53875 4577 1332 724 461 296 206 139 87 64 268 4L 43710 (88.40%) 4661 556 179 112 75 42 28 22 18 16 26

 Series 72 Champion
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Re: How many Numbers puzzles are there in total?
The stats on Apterous (which is still not a complete selection, but statistically significant) agree with the solver FAQ: http://www.apterous.org/statland.php?se ... mbers_diffJon Corby wrote:Interestingly, the percentage solvable on that Solver FAQ are less accurate than I would have expected. I wonder how big their sample size was? Or if they've made some kind of error? Because I sure as hell haven'tJon Corby wrote:Here is the breakdown by type, and how far away you can get:
Code: Select all
Zero away 1 away 2 away 3 away 4 away 5 away 6 away 7 away 8 away 9 away 10 away 11+ away 6S 1963726 (76.64%) 353472 65417 26954 15232 9859 7357 5780 4589 3945 3326 102493 1L 4966076 (95.11%) 220295 21730 5813 2527 1272 713 470 339 264 217 1676 2L 3192103 (96.23%) 112258 8487 1880 865 435 313 207 144 114 78 426 3L 693131 (91.79%) 53875 4577 1332 724 461 296 206 139 87 64 268 4L 43710 (88.40%) 4661 556 179 112 75 42 28 22 18 16 26

 Acolyte
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Re: How many Numbers puzzles are there in total?
It's the difference between a random 6 small numbers game (you) and sampling random 6 small numbers selections (apterous/solver). The unsolvable games are more likely to have a lower probability of appearing under apterous/solver due to being more likely to feature repeated numbers. Same for x large.Jon Corby wrote:Interestingly, the percentage solvable on that Solver FAQ are less accurate than I would have expected. I wonder how big their sample size was? Or if they've made some kind of error? Because I sure as hell haven'tJon Corby wrote:Here is the breakdown by type, and how far away you can get:
Code: Select all
Zero away 1 away 2 away 3 away 4 away 5 away 6 away 7 away 8 away 9 away 10 away 11+ away 6S 1963726 (76.64%) 353472 65417 26954 15232 9859 7357 5780 4589 3945 3326 102493 1L 4966076 (95.11%) 220295 21730 5813 2527 1272 713 470 339 264 217 1676 2L 3192103 (96.23%) 112258 8487 1880 865 435 313 207 144 114 78 426 3L 693131 (91.79%) 53875 4577 1332 724 461 296 206 139 87 64 268 4L 43710 (88.40%) 4661 556 179 112 75 42 28 22 18 16 26
Re: How many Numbers puzzles are there in total?
Ah yes Matthew, of course, you're absolutely right. I'm talking purely about the pool of possible distinct games, ignoring that in reality some of those are much rarer than others. Thanks, that makes perfect sense.

 Postapocalypse
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Re: How many Numbers puzzles are there in total?
Was it David Bowie?JimBentley wrote:Haha no, but I once asked one of my friends (sadly dead now I'm afraid)
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Re: How many Numbers puzzles are there in total?
Let's consider how likely that would be; (a) I didn't know David Bowie and (b) if I did I would imagine he had better things to do than write Countdown numbers game solvers for me, so (c) I wouldn't ask him to.Gavin Chipper wrote:Was it David Bowie?JimBentley wrote:Haha no, but I once asked one of my friends (sadly dead now I'm afraid)
So to conclude: No it wasn't.
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