When did "four large" become popular?

[Guy Barry]

As I mentioned in my introductory post, I hadn't seen much of the programme since the days of Richard Whiteley until recently. One thing I've noticed is that it's now far commoner for contestants to pick four large numbers - something that used to be regarded as pretty exceptional. Over the years I refined my techniques for one and two large numbers fairly well, and could usually make a reasonable stab with six small numbers, but I have to admit I still flounder when faced with those four large ones. Although in some ways I suppose it ought to be easier because you know what they are before you start.

When did this change set in? Is there any particular reason for it?

[Andy Platt]

I think I better take this one

Talking from a personal perspective, and I presume this applies for most people but I can't be sure of course, not long after I joined apterous, I realised I was a bit shit at letters and conundrums compared to naturally better (or indeed more practised) players, but pretty good at numbers as I've always been pretty good at mental arithmetic, so to make myself more competitive when playing online I was like, right, I'm going to get really good at either 6 small or 4 large to kind of capitalise on what small advantage I did have.

What made me go for 4L, and again, this is presumably the same for other players, was seeing all the clever tricks you can do involving 4 large numbers, e.g. James Martin's classic 4L solve and when I was quite new to the online game, I seem to remember Graeme Cole doing an example of what's called a 937.5 trick (hover over Jack's declaration of 936 to see his method) before I had heard of it, and it blew my mind. I wanted to learn how to do these (at least to me at the time) very impressive solutions.

After time the tricks become very intuitive, like you show anyone like Jon O'Neill, Jack Hurst, Jack Worsley, Dan McColm, etc, a solve like "100 75 50 25 3 10 @894" and they'll have solved it after a split second due to memory/intuition/experience. Most players would sit there straining themselves for 30 seconds and not get it at all. Actually, it's the same trick as in round 10 in the last-ever old-15 format, so people may be slightly more aware to it at this current moment in time, but I'd still say that most people would miss it.

Final point really about 4 large is that due to the fact it's fundamentally more difficult than 1 large and 2 large, and especially because of the fact it often relies more on recalling memory or intuition rather than raw calculation, it lends itself brilliantly to be played on TV. Calculation under pressure is harder, the memory part of your brain holds up well under pressure, and if you're playing a retired English teacher from Leamington Spa rather than a 20-year old maths student from Cambridge, I think it's safe to presume that you have the maths advantage and from a strategical standpoint, it's wise to accentuate this advantage by choosing a more outlandish numbers game.

Well, that turned into an essay pretty quickly. Jen'd be proud of me.

[Jon O'Neill]

Also: Re: Ask Graeme?

Graeme: I'm interested in how Numbers skills have evolved over the series of Countdown

Okay. Who are you, and what have you done with Matt?

specifically with regard to the Numbers round picks that contestants have selected. I seem to recall that in the early days, when Countdown was dominated by Scrabblers, it was very rare that anyone would pick anything other than 1 or 2 large. Nowadays, the 6-small specialists, and those who have put in effort to learn 4 large tricks, have come to the fore, realising how much of an advantage it confers to go for these traditionally more difficult selections.

For each series, what percentage of Numbers games have been 1 large, 2 large, 3 large, 4 large, and 6 small?

According to the database, the show was nearly seven years old before anyone thought to pick 4 large. The caveat to this is that series 1 and 2 have hardly any round details associated with them, so we can't say for certain that it didn't happen then.

Graph is as follows, but take series 1 and 2 with a pinch of salt. Only series games are included, not CoCs and specials and so on. The Supreme Championship (series 33) is included, but perhaps surprisingly the numbers picks don't seem to be much different from other series around that time. As expected, the favourite pick is 1 large, and in the very early days it was almost unheard of for anyone to pick anything other than 1 or 2 large. 6 small went through a period of being intermittently more popular than 2 large in the 1990s, but 2 large seems to have made a comeback more recently.

Also, I've not included series 67 because complete details aren't in the database. I do now have all of series 67 in machine-readable form (thanks Clive), I just haven't got round to working it into my database yet.

[Guy Barry]

What made me go for 4L, and again, this is presumably the same for other players, was seeing all the clever tricks you can do involving 4 large numbers, e.g. James Martin's classic 4L solve

Yes, I'd seen that a few times - of course it looks rather more impressive than it actually is once you mentally factor out the 25. The YouTube uploader bills it as "the most extraordinary numbers game ever", but I'd imagine that that sort of thing is relatively common now.

and when I was quite new to the online game, I seem to remember Graeme Cole doing an example of what's called a 937.5 trick (hover over Jack's declaration of 936 to see his method) before I had heard of it, and it blew my mind. I wanted to learn how to do these (at least to me at the time) very impressive solutions.

That's very good, but I have to say that the alternative solution given in the "others" column strikes me as a lot neater.

After time the tricks become very intuitive, like you show anyone like Jon O'Neill, Jack Hurst, Jack Worsley, Dan McColm, etc, a solve like "100 75 50 25 3 10 @894" and they'll have solved it after a split second due to memory/intuition/experience. Most players would sit there straining themselves for 30 seconds and not get it at all. Actually, it's the same trick as in round 10 in the last-ever old-15 format, so people may be slightly more aware to it at this current moment in time, but I'd still say that most people would miss it.

After about five minutes' careful study, I now see that the answer is (((100*75)-50)/25)*3. I suppose what I really need to do is study other people's solutions in detail to see what tricks are involved. The TV programmes don't really give you time to do this.

Final point really about 4 large is that due to the fact it's fundamentally more difficult than 1 large and 2 large, and especially because of the fact it often relies more on recalling memory or intuition rather than raw calculation, it lends itself brilliantly to be played on TV. Calculation under pressure is harder, the memory part of your brain holds up well under pressure, and if you're playing a retired English teacher from Leamington Spa rather than a 20-year old maths student from Cambridge, I think it's safe to presume that you have the maths advantage and from a strategical standpoint, it's wise to accentuate this advantage by choosing a more outlandish numbers game.

Yes, I think if you're just an armchair fan like me it's easy for a lot of the subtler methods to pass you by. I'll have to get into training!

[Jon O'Neill]

What made me go for 4L, and again, this is presumably the same for other players, was seeing all the clever tricks you can do involving 4 large numbers, e.g. James Martin's classic 4L solve

Yes, I'd seen that a few times - of course it looks rather more impressive than it actually is once you mentally factor out the 25. The YouTube uploader bills it as "the most extraordinary numbers game ever", but I'd imagine that that sort of thing is relatively common now.

I don't agree. And it's still not common.

[Gavin Chipper]

What made me go for 4L, and again, this is presumably the same for other players, was seeing all the clever tricks you can do involving 4 large numbers, e.g. James Martin's classic 4L solve

Yes, I'd seen that a few times - of course it looks rather more impressive than it actually is once you mentally factor out the 25. The YouTube uploader bills it as "the most extraordinary numbers game ever", but I'd imagine that that sort of thing is relatively common now.

I don't agree. And it's still not common.

This briefly came up in a Facebook discussion, but is his solve particularly complicated by Apterous standards? If you pick 4 large on the show, you don't always get the opportunity to get decent solves that can't also be done a more easy way, so this one certainly stands out on the show, but I wonder if that was more opportunity than anything else. Obviously it was a great solve especially since people weren't doing that sort of thing back then, but if someone did that level of solve on Apterous now, would people think that it stood out?

So it's 952 - 100, 75, 50, 25, 6, 3

To get 954 by doing (100+3)*6*75/25 is fairly basic, and he's just taken the 50 away before dividing by 25, which doesn't look that freaky to me. I'm not saying I would have got it, but it doesn't look harder to me than other people's solves. I wonder if this is because I've never really done 4-large, whereas you have so you look at the tricks and it doesn't fit one of the specific methods (e.g. it's quite near to 937.5 but doesn't use the rule for that). But then I wonder if knowing those particular rules might then hold you back in a case like this, whereas I could see someone finding the 954 and seeing how to take the 2 away. As long as you don't just get 953 and sit on it.

[Jon O'Neill]

Yes, I'd seen that a few times - of course it looks rather more impressive than it actually is once you mentally factor out the 25. The YouTube uploader bills it as "the most extraordinary numbers game ever", but I'd imagine that that sort of thing is relatively common now.

I don't agree. And it's still not common.

This briefly came up in a Facebook discussion, but is his solve particularly complicated by Apterous standards? If you pick 4 large on the show, you don't always get the opportunity to get decent solves that can't also be done a more easy way, so this one certainly stands out on the show, but I wonder if that was more opportunity than anything else. Obviously it was a great solve especially since people weren't doing that sort of thing back then, but if someone did that level of solve on Apterous now, would people think that it stood out?

So it's 952 - 100, 75, 50, 25, 6, 3

To get 954 by doing (100+3)*6*75/25 is fairly basic, and he's just taken the 50 away before dividing by 25, which doesn't look that freaky to me. I'm not saying I would have got it, but it doesn't look harder to me than other people's solves. I wonder if this is because I've never really done 4-large, whereas you have so you look at the tricks and it doesn't fit one of the specific methods (e.g. it's quite near to 937.5 but doesn't use the rule for that). But then I wonder if knowing those particular rules might then hold you back in a case like this, whereas I could see someone finding the 954 and seeing how to take the 2 away. As long as you don't just get 953 and sit on it.

You make it sound like going to 954 and working from there is the most logical thing in the world.

Actually it does fit into one of the specific methods, but there's so much other stuff you can try in this one that makes it so difficult in my opinion.

[Jon Corby]

To get 954 by doing (100+3)*6*75/25 is fairly basic

= 1,854.

Fairly basic.

[Andy Platt]

[Gavin Chipper]

Yep. Oh well.

But Jono was saying in another discussion that every time he sees the solution, it takes him a minute or so to get his head round it (presumably even when the 3 and 6 are the right way round). That's very different from just saying it's not a route you'd normally think of. Unless he just means getting his head round the idea that he picked that route.

[Jon O'Neill]

Yep. Oh well.

But Jono was saying in another discussion that every time he sees the solution, it takes him a minute or so to get his head round it (presumably even when the 3 and 6 are the right way round). That's very different from just saying it's not a route you'd normally think of. Unless he just means getting his head round the idea that he picked that route.

That's coming from the context of how I normally approach these. Which is that this is an extension of the 298/302 rule. So I guess I'm giving him too much credit when I assume that he doesn't just have the Gevin intuition that dividing by 25 will be the last step.

[David Barnard]

All I do is see how much I have to alter the end result to get to the answer when doing tricks, if the target is 313 then I'm 15 away from 298 or 11 away from 302 and work from there, part of the numbers game is to make it as simple as possible, so really I'm not working with thousands, just numbers that are around 100 maximum, this makes it easier especially on apterous where the maths is done for you, all you have to do is input the processes to get to your answer