How-To Guides

[Clare Sudbery]

I've been looking for detailed tips on how to approach the numbers game, starting with adding/subtracting before multiplying but also including more advanced techniques, basically (hopefully) culminating in a "try this, then this, then this" format, with prioritisation of more fruitful techniques over less.

So far I haven't found anything, so have started compiling my own. And here's my question:

(a) Does anyone know whether anyone has already put something like this together?

and (b) If not, what do people think about me putting something on my website? Anyone interested in contributing with tips of their own? Same could apply to letters and conundrums.

[Kirk Bevins]

Where is Stuart Earl when you need him

[Clare Sudbery]

Kirk, I just noticed the York location. I'm from York. My dad just retired from the uni.

[Michael Wallace]

Well I imagine we've all done this in our own time, but it would take one of the more hard core people to tell you if anyone's put together something like that. I'm aware of 4 large theory (which you can work out for yourself fairly easily, it starts off with knowing all the numbers you can make with just the 4 large numbers, and then moving on to the general rules that allow you to do stuff like this).

I'd be interested to know how you'd go about prioritising them on the basis of efficacy - indeed, I'm not convinced there really is all that much you can do beyond the obvious (you're quite restricted in what you're allowed to do, after all). There's also the art of balancing efficacy with ease/speed of use of the various 'methods', which would also be a nightmare to quantify.

[Kirk Bevins]

Kirk, I just noticed the York location. I'm from York. My dad just retired from the uni.

Awesome - I was wondering that when I saw your surname but I thought it would be a long shot that one of my lecturers would be related to you. When you next speak to Tony, mention my name - he'll know who I am even if he doesn't have fond memories of me!

[Clare Sudbery]

Oh yes, you can pretty much guarantee that anyone you meet in England with this surname will be directly related to me. Tis rarer than it sounds (spelt this way, that is).

I'll tell him you said hello! He's rather enjoying being retired, but I bet he'll start doing research etc again soon.

[Clare Sudbery]

You're right Michael, prioritisation would be hard. Might well be an individual thing. Maybe best just to list tips and people work out priorities for themselves. Still some things are obv higher on the list, e.g. dividing target by big numbers.

[David Williams]

You see something like this in almost every programme.

100 7 6 5 2 1 target 639

Both contestants go (6x100) + (7x5) + 2 + 1 = 638

CV gives 6x(100+5) + 7 +2 or 6x(100+7) - 2 - 1

Tip 1. Once you've made the 600 the 6 is still available to multiply by any of the other numbers (or combination thereof).

I'm firmly convinced that the average contestant would gain more points by remembering this than they would by studying word lists for a year.

Tip 2. For more difficult targets Carol often used to give solutions found by finding a factor. So in this case she might say that 639 = 9x71, and try to make 71 out of 100 6 5 1. In this case you're OK, but I'd advise strongly against this method. If you can't make 71, the best you can hope for is 9 away. This doesn't matter if you're Carol (or Rachel) because you only have to show a solution if you're spot on, but it matters a lot to a contestant.

David

[Michael Wallace]

If you can't make 71, the best you can hope for is 9 away. This doesn't matter if you're Carol (or Rachel) because you only have to show a solution if you're spot on, but it matters a lot to a contestant.

This is a good point, and something easily overlooked by the average viewer (or at least, something I'd overlooked). If I'm watching at home I tend to just go for spot-on, because a) it's probably solvable, and ii) I'm not (really) competing against the contestants. It was something I noticed when I started playing on apterous - suddenly getting 1 away quickly (if you can) is quite important, and going all out for spot on can often leave you with a frantic 10 seconds at the end trying to find *something*.

Approach will obviously depend a lot on the selection. If it's 4 large then there's not much you can do (and so what is is fairly well documented). If it's 6 small I tend to look at the biggest small and aim for the target - if there's a 9 and the target is, say, 789, then it's fairly easy (and quick) to work out that making 87 or 88 from the remaining numbers would be a good start. With 1 large the main difficulty (I find) is when the large is 25, but splitting up the multiplication can often be quite fruitful - if the target is near 900 and you've got a 4 and 9 then you can add/subtract a small number before the 4 multiplication or the 9 multiplication (or both, if it's not-so-close to 900).

I'm not really sure how much of this counts as non-obvious, though - and I like David's point about contestants learning the adding to the large before multiplying probably doing them a great deal of good. I find the numbers performances on the show pretty poor (sometimes staggeringly, but perhaps that's just me being biased towards the numbers, and we can all have bad days) - I don't know how much one can improve one's speed at mental arithmetic with practice, but that alone would probably be a great help to a lot of contestants too (plus times tables - I think one of the biggest problems my fiance has when watching is that he hasn't played/watched enough Countdown to just 'know' what multiple of the large number you need to get close to the target, in the same way you just 'know' that 7x8 = 56, without having to work it out).

[Kirk Bevins]

Knowing your 4 times table helps because when you have a 25 in the selection and the target is say 937 and you want to know how many 25s get you close to 937, always multiply the hundreds digit of the target by 4 then add on 25s. For example, 937 is 9x4=36 lots of 25s to get the 900 then I can add on one or two 25s to get close. Thus I'm looking for 37 or 38 lots of 25s.

The more advanced one large solutions involve split multiplication as Michael alluded to. Suppose the target is 932 and the numbers are: 25, 1, 4, 9, 8, 8.
I notice I can do 25x9x4 and then add on 8x4. Putting this altogether gives me: (25x9+8) lots of 4. Can look quite impressive when you explain your solution and end up doing 233x4 as the majority of the viewers won't have known your original thinking as to why to look to go that way.

This method can be used (i.e. timesing by a number, then adding/subtracting another number, then multiplying again) when your multiple of 25 is not prime and can be in fact made from directly multiplying two small numbers, e.g. 4x9 gives me the 36 (so I can go x4, add something, x9 OR go x9, add something and x4). This may sound obvious but is sometimes overlooked. When I work out what I have to times the 25 or the 50 (say) by and it turns out it's something like 32 and I have a 4 and an 8 in the selection, my first instinct is this split multiplication as it saves using a number or two.

It's actually quite hard explaining over the internet different methods but I hope at least one person follows the above.

[Clare Sudbery]

Yup, I followed all of that. Am already using most of that but there's some new stuff in there, particularly the stuff about looking for factors of the target (ie be wary).

Certainly the single most useful technique I use is the addition / subtraction before multiplication, as well as the mid-multiplication addition/subtraction when your target multiple isn't prime (as you say, most used when you have a 25).

This is all really useful stuff, keep it coming! When this thread runs out of steam I'll collate it all in a handy guide and link to it.

As for how much you can improve your numbers skills... the answer is a LOT. Certainly you can improve speed of mental arithmetic with practice, and obv learning times tables helps.

Doesn't surprise me at all that many contestants struggle with the numbers round. Countdown is primarily a word game, and there are millions of people out there who go nutty for words but have no arithmetical aptitude. One of the reasons I like it is that I go nutty for both words AND numbers.

What about words and conundrums? I'd advise stuff like:
- Write the letters down. It takes time but you might find it much easier to think about it if, for instance, you write the letters in a circle. I'd been avoiding do it on Apterous cos of the time loss, but when I started doing it my results improved.
- When writign letters in a circle, write first letter at 12 o'clock, next two adjacent at 6 o'clock, next six at (approx) 11, 1, 7, 5, 9 and 3. That way you get a neat circle quickly and letters are automatically shuffled, which is useful for conundrum.
- Look for common endings (ING, ED, AGE, MENT, NESS etc) but only allow a few seconds for each one. Don't get too obsessed.
- Look for compound words (HANDBAG, BOYFRIEND, COWPOKE etc).

And for all rounds:
- Whenevr you find yourself panicking or despairing, take deep breath, try to relax, pretend you're in armchair at home
- conundrum: keep finger on buzzer, remember to press. Horribly easy to forget this.
- don't get distracted. Rounds will start quickly and you might not be ready.
- don't pay attention to score. Do like pro tennis players - each point is the only point being played. Forget past or future.

I have a giant list of numbers tips I've been making as I go along - includes some of the stuff mentioned above. Will try and transcribe it here soon, but am short on time, sorry.

[Clare Sudbery]

Also for words: Be prepared to try new techniques. For instance I was sceptical about the circle technique, btu it really works (for me), as all letters are as close to all other letters as is possible, so you spot combinations you may miss otherwise

Oh and: try scoring out promising-looking endings (ING being the obvious one) so you can see what's left. Actually no, don't do this. It mucks up your ability to see any other kind of word. Instead, write out the remaining letters elsewhere. Can be time consuming though - approach with caution.

[Kirk Bevins]

And for all rounds:
- Whenevr you find yourself panicking or despairing, take deep breath, try to relax, pretend you're in armchair at home
- conundrum: keep finger on buzzer, remember to press. Horribly easy to forget this.
- don't get distracted. Rounds will start quickly and you might not be ready.
- don't pay attention to score. Do like pro tennis players - each point is the only point being played. Forget past or future.

I have a giant list of numbers tips I've been making as I go along - includes some of the stuff mentioned above. Will try and transcribe it here soon, but am short on time, sorry.

Interesting you're advising this and you've not actually experienced the pressure yourself yet!

I would actually advise against your last bullet point. I always like to know what the score is so I can play tactically - i.e go 4 large or 1 large accordingly. What you actually mean is: Don't let a bad past word or missed word get to you. Forget about it and move on.

[Michael Wallace]

I would actually advise against your last bullet point. I always like to know what the score is so I can play tactically - i.e go 4 large or 1 large accordingly. What you actually mean is: Don't let a bad past word or missed word get to you. Forget about it and move on.

Yeah. Score is also clearly relevant when you're declaring - if you're 21 points behind in the last letters game and your opponent declares 6 and you have a dodgy 7 being the most straightforward example.

[David Williams]

Totally agree. And, unless things have changed, you can't see the score, so keep a note of it.

The other thing you can't see is your opponent's name plate. When I was on there was no Green Room, just separate male and female changing rooms. My first show was the first of the day, so the first time I set eyes on my (female) opponent was on the set. She was very friendly, gave me a few little tips about what actually being on set was like, and we had a good chat during half time. In the second half Richard asked me a question to which the answer was "Well, X was saying to me in the break . . ." As I said "Well" I realised I had no idea what her name was! After that I always wrote it down. Not a big thing, but anything that makes you that little bit more comfortable helps.

David

[David Roe]

Write down at least 2 copies, possibly 3 copies, of the letters as Rachel declares them. Then you can cross out likely endings like ING, and have a clean set of letters to go to if ING doesn't work.

[Jon Corby]

Write down at least 2 copies, possibly 3 copies, of the letters as Rachel declares them. Then you can cross out likely endings like ING, and have a clean set of letters to go to if ING doesn't work.

I tear each sheet of paper into 10 small pieces, and write a letter clearly on each, and "STOP" on the tenth. Then during the 30 seconds I fold each one up, shake them around in my fist, and toss them onto the table. I then arrange them in the order they have fallen, and unfold each one in turn until I hit "STOP". Thus my declaration is spelt out. It sounds daft, but it worked quite well for me. It also rules out declaring any word with phantom/wrongly duplicated letters, which would be embarrassing.

[Clare Sudbery]

Jon, I don't understand. It sounds as though you are tossing them randomly, in which case STOP could be unfolded at any point? And yet you seem to be talking about declaring the word you have found, in which case i still can't see the point of 'STOP'. I'm obviously not getting what you mean.

[Clare Sudbery]

kirk, altho i haven't been on, i have experienced the effect pressure has on me on apterous. also from being on different quiz show in the 80s (connections, granada, kids tv, i was 16) i learnt some general stuff. good point re scores.

[Clare Sudbery]

i've also been wondering about word lists. i know scrabble players have lists of most common letter combinations, but that depends on letter frequencies. anyone know letter frequencies on countdown? are all letters equally likely to appear? anyone got useful word lists?

[apols for poor typing, have wriggly baby on knee]

[Peter Mabey]

Tip 2. For more difficult targets Carol often used to give solutions found by finding a factor. So in this case she might say that 639 = 9x71, and try to make 71 out of 100 6 5 1. In this case you're OK, but I'd advise strongly against this method. If you can't make 71, the best you can hope for is 9 away. This doesn't matter if you're Carol (or Rachel) because you only have to show a solution if you're spot on, but it matters a lot to a contestant.

David

As I can usually spot the factorisation (if any) of the target immediately, I often fall into this trap when playing at home - e.g. seeing that 493=17x29=(50+1)x(25+4)/3 would be nice, but if the numbers aren't helpful, I could miss a way of doing 500-7.

[Malcolm James]

On the numbers, working backwards, i.e. by factorising the target number, can work well and reveal solutions which you wouldn't find by working forward, but it does have the disadvantage, as has been pointed out, that if you can't hit the final factor spot-on, you don't have anything to declare. If you're faced with a target which looks difficult, try factorising a nearby number which does factorise. There are three advantages of this.
1. The target may be impossible and you've found the best solution.
2. You avoid the panic of getting 25 seconds in and having nothing to declare. Even if the game is solvable, you may well have done enough to get 7 points.
3. You may get a nice surprise!

Example:

Some precocious git goes for 6 small and the numbers are 9,6,5,3,1,1. Cecil produces a target of 971. Cue despair from Rachel and contestants, since 971 is prime. 972 is a much friendlier number, so:
972/9 = 108
108/6 = 18
18/3 = 6
5 + 1 = 6
And you still have the second 1!

Even if the target is 917, you can try factorising 918.
918/9 = 102
102/6 = 17
((5 + 1) x 3) - 1 = 17

Having found that (hopefully fairly quickly) you can probably think more rationally for the rest of the time and realise that 917 = 131 x 7. 6 + 1 = 7, so you look for 131 with the remaining numbers. As far as I can see, it's not possible, and 918 is the best you can do, and you will get 7 points.

[Jon O'Neill]

Just PRACTISE and eventually you will be good!

[David Roe]

Some precocious git goes for 6 small and the numbers are 9,6,5,3,1,1. Cecil produces a target of 971. Cue despair from Rachel and contestants, since 971 is prime. 972 is a much friendlier number, so:
972/9 = 108
108/6 = 18
18/3 = 6
5 + 1 = 6
And you still have the second 1!

Alternative way of getting the same result: multiply up the small numbers to get somewhere near. Eg. 9 x 6 x 5 x 3 = 810, so adding 1 to the 5 adds an extra (9 x 6 x 3, 162) to the total for 972. My problem is running out of time - if I'd guessed at adding 1 to the 6 instead of the 5, I'd have probably missed out altogether. But I do tend to work from the bottom up to the solution, not from the solution down.

[David O'Donnell]

Just PRACTISE and eventually you will be good!

Some quality advice from a quality player. It's interesting that in this "how to" thread most of the contributions are from people who are yet to actually try their hand at the show for real (barring David Williams and now, Jono).

[Clare Sudbery]

If someone were learning to play an instrument, would you advise them to take lessons AND practise, or concentrate on practice alone? There's nothing wrong with injecting a little focus into your practice, but obviously none of these techniques are any use without it.

[Clare Sudbery]

Tell you what though, I won't write any of this up until I've been on the show. Then we'll all be happy. :O)

[Jon Corby]

Just PRACTISE and eventually you will be good!

Some quality advice from a quality player. It's interesting that in this "how to" thread most of the contributions are from people who are yet to actually try their hand at the show for real (barring David Williams and now, Jono).

Oi

[Michael Wallace]

Some quality advice from a quality player. It's interesting that in this "how to" thread most of the contributions are from people who are yet to actually try their hand at the show for real (barring David Williams and now, Jono).

Oi

Yeah, just because Corby and I are rubbish isn't a good excuse for forgetting we've been on the show too.

[David Williams]

You will be good - eventually. But most contestants know they aren't going to be series champion, and would be more than happy to win just once. They aren't going to commit hours and hours to practising, but they might be helped by a few tips to suggest the most productive use of a bit of spare time.

I would have done that 917 in very similar fashion. 917/9 is about 100. 100/6 is about 17. So what's 9x6x5x3? 810 and I've only two 1's left. How can I get most of that with one of them? By multiplying 1 by 6x5x3. So what's (9+1)x6x5x3? 900. How near can I get to 17? By multiplying the other 1 by 6x3. So I've got ((9+1)x5+1)x6x3 = 918.

Not foolproof, but I think learning the method and practising that, rather than just practising, would pay dividends for lots of people.

David

[Gavin Chipper]

Jon, I don't understand. It sounds as though you are tossing them randomly, in which case STOP could be unfolded at any point? And yet you seem to be talking about declaring the word you have found, in which case i still can't see the point of 'STOP'. I'm obviously not getting what you mean.

By having STOP, it gives him the chance of a 13-letter word.

[Clare Sudbery]

"By having STOP, it gives him the chance of a 13-letter word."

LOL!

[Craig Beevers]

Alternative way of getting the same result: multiply up the small numbers to get somewhere near. Eg. 9 x 6 x 5 x 3 = 810, so adding 1 to the 5 adds an extra (9 x 6 x 3, 162) to the total for 972. My problem is running out of time - if I'd guessed at adding 1 to the 6 instead of the 5, I'd have probably missed out altogether. But I do tend to work from the bottom up to the solution, not from the solution down.

That's pretty much the sort of thing I did when practising 6 small - I'd get just look at 3-4 numbers which would get somewhere close. I also tended to do multiple additions/subtractions.

Like say with 9 6 5 3 1 1 and you needed 860. I'd go right 9x6x5x3 = 810. I can get an extra 45 from using the 9x5. From there I can use either 9 or 5 again, or (6x3 + 1) ie 19. Obviously you need to use the 5. So it ends up being 6x3 + 1 = 19. 19 * 9 = 171. 171 + 1 = 172. 172 * 5 = 860. This gives you a lot of combinations and you can usually get close.

For this I'd write 9 6 5 3 = 810, then I'd have a line connecting the 9 & 5 with a +1 on it (as you're adding 1 for that, as opposed to taking it away and ending up with 765), then another line pointing just to the 5 with +1 on it. Developing a shorthand way of writing workings out is handy.

I'd also think finding a mental arithmatic game you like and having a short stints on it is well worth it. I used to do a quick 10-15 minutes on Meteor Multiplication on Arcademic Skill Builder's site. You will get significantly faster at the basic calculations with little effort and this will give you extra seconds thinking time whilst making you less likely to mess up as well.

[Kirk Bevins]

I'd also think finding a mental arithmatic game you like and having a short stints on it is well worth it. I used to do a quick 10-15 minutes on Meteor Multiplication on Arcademic Skill Builder's site. You will get significantly faster at the basic calculations with little effort and this will give you extra seconds thinking time whilst making you less likely to mess up as well.

Can you link us please Craig - this may be useful to use in lessons.

[Charlie Reams]

I'd also think finding a mental arithmatic game you like and having a short stints on it is well worth it. I used to do a quick 10-15 minutes on Meteor Multiplication on Arcademic Skill Builder's site. You will get significantly faster at the basic calculations with little effort and this will give you extra seconds thinking time whilst making you less likely to mess up as well.

Can you link us please Craig - this may be useful to use in lessons.

This took, like, 2 seconds on Google. Maybe you should teach your students how to find information out for themselves...

[Kirk Bevins]

I'd also think finding a mental arithmatic game you like and having a short stints on it is well worth it. I used to do a quick 10-15 minutes on Meteor Multiplication on Arcademic Skill Builder's site. You will get significantly faster at the basic calculations with little effort and this will give you extra seconds thinking time whilst making you less likely to mess up as well.

Can you link us please Craig - this may be useful to use in lessons.

This took, like, 2 seconds on Google. Maybe you should teach your students how to find information out for themselves...

Haha brilliant. I'm ultra lazy and when I posted it I thought "I could have just looked that up on Google" but thanks for explicitly pointing that out.

[Clare Sudbery]

Conundrums: If you find a convincing but nonsensical solution, like LOVESTICK or MINEWHALE, try a little spoonerisation* before giving up altogether or declaring a patently silly word!

*LIVESTOCK, MEANWHILE.

[Dinos Sfyris]

Dont talk to me about MEANWHILE!

[Clare Sudbery]

Eh? Can you elucidate?

[Charlie Reams]

Eh? Can you elucidate?

http://www.countdownwiki.com/Episode_4460

[Dinos Sfyris]

Sure thing http://www.apterous.org/cdb/game.php?game=1230

[Jon Corby]

Dont talk to me about MEANWHILE!

Just think, if only you'd met Clare before this, you could have gone on to be the greatest player ever...

[Clare Sudbery]

Ah, I see. Bad luck.

By the way, meant to come back here and pedanticise aganst myself... tis not a Spoonerism, I think, if it's visual rather than aural.

MINEWHEAL would be a Spoonerism. Although I'm also not sure whether Spoonerisms can be worked against vowels as well as consonants. But I think they can. I thank they kin, too. ;o)

[Phil Reynolds]

MINEWHEAL would be a Spoonerism. Although I'm also not sure whether Spoonerisms can be worked against vowels as well as consonants. But I think they can. I thank they kin, too. ;o)

Indeed they can, as when the eponymous Reverend himself is supposed to have sung in the college chapel, "Kinkering kongs their titles take".

[Clare Sudbery]

Watch out for RE/ER, DE/ED, and combinations thereof. For instance with REER you might get REENTER, with REED get DERIDER (um, I think) or REMADE, etc...

[Clare Sudbery]

Another nice rule:

37 * 3 = 111, so any target with three identical digits can be factorized that way.

[edited significantly]

[cough]

[Michael Wallace]

From Martin Gardner here:

Yeah, way to link to a spoilers thread with no warning.

Another tip for conundrums: rearrange the 9 letters to form a word.

[Martin Gardner]

I hadn't actually spotted this thread before. Anyway, I suppose 'just practise' is a good idea, but isn't it interesting to compare methods anyway?

For letters, it depends on what type of person you are. Funnily reading the 'do you learning meanings of words' thread I've changed my mind quite a lot. I think my method only works for people that process words like me (Stewart Holden is possibly the only player who's more mathematical than I am!). You probably don't have to learn *that* many words for Countdown, I had barely done any word learning before I went on, I just used all the stuff that Dictionary Corner came up with. Nothing like Countmax existed at the time, so I used to put letters into Andy's Anagram Solver and then check against the NODE (that is, the ODE when it was still new).

This reminds me of a conversation I was having with a former (French) World Scrabble Champion who say's it's not all about knowing the words, it's about being able to recall them as well. So when you learn a word, you need some method of recalling it. Definitions do help, but I find WORD + LETTER is much easier to spot. So NURAGHE is just HUNGER + A. So every time that I see HUNGER in a letters game, I check to see if there's an A with it. It's no exaggeration to say that I have a few thousand of these. But as I indicated above, that doesn't work for everbody. I haven't particularly put effort into learning all that, it's just how my brain does it. I suppose the problem with learning definitions for this purpose, is the words are isolated and not linked to each other.

*NURAGHE is invariable, no NURAGHES^

[Clare Sudbery]

"Yeah, way to link to a spoilers thread with no warning."

Oh help, I'm really sorry. Still learning the ropes. Will un-link.

[Clare Sudbery]

"rearrange the 9 letters to form a word."

:O)

[Martin Gardner]

Paul Howe on another thread mentioned about just "recalling" the words rather than using your actual angramming ability (after I brought it up first, I mean). I had a little think about this, and I'm not sure the two are actually different things. When you've done so much practice for the game, the process just gets so fast you don't even know you're doing it, so when AEDRLTO comes out as the first 7 letters, I automatically see LEOTARD/DELATOR. I'm still doing the anagram, it's jus so fast that I don't notice it. That being said, I think looking for structure is good as well; what I do at home (that I couldn't do in the studio) is make up some completely fictional words just to pronounce the letters, which might make me think of a word that sounds similar. Admittedly, I'm not sure if that's ever worked for me, ever! But still...

[Gavin Chipper]

"Yeah, way to link to a spoilers thread with no warning."

Oh help, I'm really sorry. Still learning the ropes. Will un-link.

It's probably more the quote from it than the link to it that was the problem.

[Clare Sudbery]

Oh God. I have been truly hit with the dim stick. Right. Yes. Um. OK...

[goes back to edit again]

[Kai Laddiman]

Another tip for conundrums: rearrange the 9 letters to form a word.

Damn. Maybe I should try that technique in the future. Raccoon Boy

[Michael Wallace]

Damn. Maybe I should try that technique in the future. Raccoon Boy

You'd be surprised how many people overlook it (maybe it's a bit too subtle an approach?).

[Dinos Sfyris]

Damn. Maybe I should try that technique in the future. Raccoon Boy

You'd be surprised how many people overlook it (maybe it's a bit too subtle an approach?).

GERANIUMS!

[Junaid Mubeen]

That's pretty much the sort of thing I did when practising 6 small - I'd get just look at 3-4 numbers which would get somewhere close. I also tended to do multiple additions/subtractions.

Like say with 9 6 5 3 1 1 and you needed 860. I'd go right 9x6x5x3 = 810. I can get an extra 45 from using the 9x5. From there I can use either 9 or 5 again, or (6x3 + 1) ie 19. Obviously you need to use the 5. So it ends up being 6x3 + 1 = 19. 19 * 9 = 171. 171 + 1 = 172. 172 * 5 = 860. This gives you a lot of combinations and you can usually get close.

For this I'd write 9 6 5 3 = 810, then I'd have a line connecting the 9 & 5 with a +1 on it (as you're adding 1 for that, as opposed to taking it away and ending up with 765), then another line pointing just to the 5 with +1 on it. Developing a shorthand way of writing workings out is handy.

Yup, that pretty much sums up my 6 small strategy. Note that if you use 4 numbers as factors and split the multiplication twice, as in Craig's example above, your final operation is multiplication, which means you are reduced to finding a target with 5 numbers. In the above, Craig's method is reduced to 172x5 and you are left to find 172 with 9,6,3,1,1. The drawback comes when your target isn't divisible by one of the numbers you have.

If, however, you only use 3 factors you have more scope, as you can split the multiplication twice AND add/subtract at the last stage. This is particularly handy if, for example, the target is prime or, more generally, has no prime factors less than 10 (and so certainly none of the 6 small numbers).

In most cases, I find that splitting the multiplication once is enough, certainly to get within 10 of the target.

THE FOLLOWING CONTAINS TRACES OF ABSTRACT MATHEMATICS (you have been warned).

For anyone who cares, the 'one split' method can be summarised by

abc+nb+p = b(ac+n)+p (1)

whilst the 'two split' can be summarised by

abc+nbc+mc+p=c((a+n)b+m)+p (2)

In equation (2), a,b,c are the factors used to get 'close' to the target. m and n are the mutiples used to split the factors. p is the bit you add/subtract at the end. Equation (1) is similar. Of course, n, m and p can take the value 0. The expressions on the RHS show that we are ok with respect to Countdown rules in that we are only using the numbers once each.

For example, with 6 small if there is a 10 most people attempt to use it in the obvious way. Let's say the target is 293 and the numbers are 7,4,1,10,3,8. I think most people would do something like (7x4+1)x10+3, right?

What you have actually done is to say 7x4x10=280 and then you have negotiated the extra 13 by first splitting the factor of 10 (that's when you add the 1 to 28) and then adding on the 3 at the end. So looking at equation (1), we have chosen a=7,b=10,c=4,n=1,p=3. In other words, your choice of 'b' determines which factor you split. Most people naturally go for b=10 if 10 is available since it's relatively easy to deal with, as in the 293 example. However, the power of this more general method is that you can choose b to be any of the inital factors you have used. In the 293 example, you can also take b=7 or b=4(details left as an exercise). So the 6 small method illustrated by equation (1) is a generalisation of the obvious method commonly used, and its power comes in being able to choose from so many factors, not just 10. When I miss a target, it's usually because I've backed the wrong factor to split or even the wrong initial factors.

I should say that I don't use a's, b's and c's whilst actually playing. They were just used to illustrate the method to anyone who wanted it in generality.

Essentially though, you do need good mental arithmetic, just to be able to deal with factors other than 10. And a bit of intuition to know which factors to play with (yes, play), although that certainly improves with practise. e.g. if the target is near 500 I look for 7,8 and 9 since 7x8x9=504.

Wow, my longest and probably most boring post to date.

[Jimmy Gough]

Just PRACTISE and eventually you will be good!

Seriously? You don't use any other methods for improvement? Surely there's a lot more to it to be that good?

[Jimmy Gough]

Another nice rule:

37 * 3 = 111, so any target with three identical digits can be factorized that way.

[edited significantly]

[cough]

Sorry, sorry, sorry for being stupid. I still don't understand how this works??

[Junaid Mubeen]

Another nice rule:

37 * 3 = 111, so any target with three identical digits can be factorized that way.

[edited significantly]

[cough]

Sorry, sorry, sorry for being stupid. I still don't understand how this works??

aaa = 111xa = 3x37xa where a is a whole number between 1 and 9.
So given a target of aaa, you just need to make the numbers 3, 37 and a from the ones that you have.