How many Numbers puzzles are there in total?

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Peter Clarke
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How many Numbers puzzles are there in total?

Post by Peter Clarke » Wed Jan 06, 2016 10:14 pm

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 1-10 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 (999-101=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 0-9 (10 numbers) and there are six of one number each (filling all gaps). In this case, there are two of numbers 1-10 each and 25, 50, 75, 100.

Hope you all get what I mean, apologies if I haven't been clear.

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Re: How many Numbers puzzles are there in total?

Post by Conor » Wed Jan 06, 2016 11:20 pm

.
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?

Post by Fred Mumford » Wed Jan 06, 2016 11:21 pm

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.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Wed Jan 06, 2016 11:23 pm

There's four per episode.

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Re: How many Numbers puzzles are there in total?

Post by Thomas Carey » Wed Jan 06, 2016 11:45 pm

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
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Re: How many Numbers puzzles are there in total?

Post by Gavin Chipper » Wed Jan 06, 2016 11:46 pm

Peter Clarke wrote:and then multiply by the amount of targets which is 898 I think (999-101=899 ).
Is that the wrong way round?

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Re: How many Numbers puzzles are there in total?

Post by Fred Mumford » Wed Jan 06, 2016 11:52 pm

Thomas Carey wrote:Fuck's sake Fred
Ah yes, the Bernard Cribbins follow up single that got banned.

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Re: How many Numbers puzzles are there in total?

Post by Peter Clarke » Thu Jan 07, 2016 12:02 am

Oh yeah there are 899 targets, so 999-100=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?

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Re: How many Numbers puzzles are there in total?

Post by Thomas Carey » Thu Jan 07, 2016 12:04 am

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?

Post by Gavin Chipper » Thu Jan 07, 2016 12:06 am

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 don't believe you could do all that including typing in 10 minutes!

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Re: How many Numbers puzzles are there in total?

Post by Thomas Carey » Thu Jan 07, 2016 12:11 am

Gavin Chipper wrote:
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 don't believe you could do all that including typing in 10 minutes!
Yeah probably like 20 who care
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Re: How many Numbers puzzles are there in total?

Post by Jack Worsley » Thu Jan 07, 2016 4:52 am

Thomas Carey wrote:Right. I'm probably gonna make about a hundred arithmetic errors
No, just this one, and quite a bad one as well.

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.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Thu Jan 07, 2016 8:44 am

Fred Mumford wrote:
Thomas Carey wrote:Fuck's sake Fred
Ah yes, the Bernard Cribbins follow up single that got banned.
:lol:

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Thu Jan 07, 2016 8:49 am

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 three-dimensional reporting cube please. 15 minutes.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Thu Jan 07, 2016 12:53 pm

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?

Post by Gavin Chipper » Thu Jan 07, 2016 2:41 pm

Gavin Chipper wrote:
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 don't believe you could do all that including typing in 10 minutes!
Conor wrote:.
I can believe that this was completed inside 10 minutes by the way.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Thu Jan 07, 2016 4:00 pm

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.
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?!

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Thu Jan 07, 2016 4:05 pm

Jon Corby wrote:
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.
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?!
Didn't William Tungsten-Paedo 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.

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Re: How many Numbers puzzles are there in total?

Post by Philip Wilson » Thu Jan 07, 2016 4:36 pm

But what about when 6s and 9s can come out upside down like Ms and Ws do? That must change the numbers available :-)

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Thu Jan 07, 2016 4:44 pm

JimBentley wrote:
Jon Corby wrote:
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.
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?!
Didn't William Tungsten-Paedo 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.
Wanna link me up? I don't fancy searching for somebody called Peado while I'm at work...

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Thu Jan 07, 2016 4:51 pm

Jon Corby wrote:
JimBentley wrote:Didn't William Tungsten-Paedo 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.
Wanna link me up? I don't fancy searching for somebody called Peado while I'm at work...
I may have intentionally misremembered his name for comedy value. Anyway, here you go:

http://www.crosswordtools.com/numbers-game/faq.php

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Thu Jan 07, 2016 6:26 pm

JimBentley wrote:
Jon Corby wrote:
JimBentley wrote:Didn't William Tungsten-Paedo 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.
Wanna link me up? I don't fancy searching for somebody called Peado while I'm at work...
I may have intentionally misremembered his name for comedy value. Anyway, here you go:

http://www.crosswordtools.com/numbers-game/faq.php
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.

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Thu Jan 07, 2016 6:32 pm

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.
Hey, I never said there would be anything of value there, I think the guy's a bit of a dick anyway.

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?

Post by Peter Clarke » Fri Jan 08, 2016 12:04 am

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?

Post by Jack Worsley » Fri Jan 08, 2016 5:36 am

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?
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.

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Re: How many Numbers puzzles are there in total?

Post by Peter Clarke » Fri Jan 08, 2016 5:42 am

Jack Worsley wrote:
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?
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.
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).

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?

Post by Graeme Cole » Fri Jan 08, 2016 9:27 am

Peter Clarke wrote:
Jack Worsley wrote:
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?
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.
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).

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.
Yes. Sometimes you can see Rachel using the clipboard if it's a difficult round.

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Re: How many Numbers puzzles are there in total?

Post by Philip Wilson » Fri Jan 08, 2016 11:04 am

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?

Post by Jon Corby » Fri Jan 08, 2016 11:17 am

Philip Wilson wrote:From RRs reactions to the crew sometimes it looks like she is probably told easy ones are possible sometimes!
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 near-as-possible (and she'll often say that she was n away).

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Re: How many Numbers puzzles are there in total?

Post by Thomas Carey » Fri Jan 08, 2016 1:28 pm

JimBentley wrote:
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.
Hey, I never said there would be anything of value there, I think the guy's a bit of a dick anyway.

I'm sure someone's done this thoroughly, though, I just can't quite remember who.
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.

Do you want to know which ones are solvable, one away etc or just how many?
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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Fri Jan 08, 2016 1:38 pm

Thomas Carey wrote:
JimBentley wrote:
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.
Hey, I never said there would be anything of value there, I think the guy's a bit of a dick anyway.

I'm sure someone's done this thoroughly, though, I just can't quite remember who.
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.

Do you want to know which ones are solvable, one away etc or just how many?
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...

Also, who is this (on the left) from the solver page that Jim linked to:

Image

?

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Fri Jan 08, 2016 1:45 pm

Jon Corby wrote:Also, who is this (on the left) from the solver page that Jim linked to:

Image

?
I think she was called something like Ariane or something, she was a stand-up 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.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Fri Jan 08, 2016 1:52 pm

JimBentley wrote:
Jon Corby wrote:Also, who is this (on the left) from the solver page that Jim linked to:

Image

?
I think she was called something like Ariane or something, she was a stand-up 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.
Is that Philpot in the picture as well?

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Fri Jan 08, 2016 2:13 pm

Jon Corby wrote:
JimBentley wrote:
Jon Corby wrote:Also, who is this (on the left) from the solver page that Jim linked to:

Image

?
I think she was called something like Ariane or something, she was a stand-up 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.
Is that Philpot in the picture as well?
Pretty sure so, he posted quite a bit at the time about it.

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Re: How many Numbers puzzles are there in total?

Post by Gavin Chipper » Fri Jan 08, 2016 3:13 pm

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?

Post by Thomas Carey » Fri Jan 08, 2016 3:18 pm

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.
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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 8:08 am

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...
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 brute-forced 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.

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?

Post by Gavin Chipper » Mon Jan 11, 2016 9:56 am

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?
This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 10:04 am

Gavin Chipper wrote:
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?
This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.
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.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 1:51 pm

Gavin Chipper wrote:
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?
This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.
That is just one of 1,226 selections which can be maxed with every possible target from 101-999.

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?

Post by Dan McColm » Mon Jan 11, 2016 1:57 pm

Jon Corby wrote:
Gavin Chipper wrote:
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?
This has come up before and the answer's yes. From memory maybe 100, 1, 3, 5, 7, 9.
That is just one of 1,226 selections which can be maxed with every possible target from 101-999.

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.
I'll guess that 9, 4, 5, 2, 3, 8 is one of the 6 smalls?

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Re: How many Numbers puzzles are there in total?

Post by Graeme Cole » Mon Jan 11, 2016 2:11 pm

What about the same question the other way round... which targets are solvable by every 1-large selection? Every 2 large? 3 large? 4 large?

Which target is solvable by the fewest selections?

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Re: How many Numbers puzzles are there in total?

Post by Gavin Chipper » Mon Jan 11, 2016 2:16 pm

Graeme Cole wrote:What about the same question the other way round... which targets are solvable by every 1-large selection? Every 2 large? 3 large? 4 large?

Which target is solvable by the fewest selections?
You're not allowed to ask questions!

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Re: How many Numbers puzzles are there in total?

Post by Thomas Cappleman » Mon Jan 11, 2016 2:22 pm

Graeme Cole wrote:What about the same question the other way round... which targets are solvable by every 1-large selection? Every 2 large? 3 large? 4 large?

Which target is solvable by the fewest selections?
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).

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Mon Jan 11, 2016 2:42 pm

Dan McColm wrote:
Jon Corby wrote:That is just one of 1,226 selections which can be maxed with every possible target from 101-999...

5 are 6 small.
I'll guess that 9, 4, 5, 2, 3, 8 is one of the 6 smalls?
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).

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 2:52 pm

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?

Post by Jon Corby » Mon Jan 11, 2016 2:57 pm

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

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Mon Jan 11, 2016 2:57 pm

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.)
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).

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 3:03 pm

Graeme Cole wrote:What about the same question the other way round... which targets are solvable by every 1-large selection? Every 2 large? 3 large? 4 large?
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, 450
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

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 3:09 pm

Graeme Cole wrote:Which target is solvable by the fewest selections?
947, but even then there 9,017 selections which solve and only 4,226 which do not.
It's then small steps to the next worst, 941 (9045 solve, 4,198 don't), and similarly onto 967, 933 and 937 (T-Cap'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)

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 3:13 pm

Dan McColm wrote:
Jon Corby wrote: That is just one of 1,226 selections which can be maxed with every possible target from 101-999.

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.
I'll guess that 9, 4, 5, 2, 3, 8 is one of the 6 smalls?
This selection has 41 unsolvable targets:

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?

Post by JimBentley » Mon Jan 11, 2016 3:14 pm

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?

Post by Jon Corby » Mon Jan 11, 2016 3:18 pm

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).
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.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 3:26 pm

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.
I have no fucking idea what is significant about 961 by the way, if that helps anyone.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 3:32 pm

Jon 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
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't :x

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Re: How many Numbers puzzles are there in total?

Post by Thomas Cappleman » Mon Jan 11, 2016 3:39 pm

Jon Corby wrote:
Jon 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
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't :x
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_diff

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Re: How many Numbers puzzles are there in total?

Post by Matthew Tassier » Mon Jan 11, 2016 3:43 pm

Jon Corby wrote:
Jon 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
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't :x
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.

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Re: How many Numbers puzzles are there in total?

Post by Jon Corby » Mon Jan 11, 2016 3:47 pm

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.

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Re: How many Numbers puzzles are there in total?

Post by Gavin Chipper » Mon Jan 11, 2016 4:07 pm

JimBentley wrote:Haha no, but I once asked one of my friends (sadly dead now I'm afraid)
Was it David Bowie?

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Re: How many Numbers puzzles are there in total?

Post by JimBentley » Mon Jan 11, 2016 4:41 pm

Gavin Chipper wrote:
JimBentley wrote:Haha no, but I once asked one of my friends (sadly dead now I'm afraid)
Was it David Bowie?
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.

So to conclude: No it wasn't.

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