The Surprising Maths of Britain's Oldest* Game Show
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- čas přidán 7. 06. 2024
- ⬣ LINKS ⬣
⬡ PATREON: / anotherroof
⬡ CHANNEL: / anotherroof
⬡ WEBSITE: anotherroof.top
⬡ SUBREDDIT: / anotherroof
⬣ ABOUT ⬣
First broadcast in 1982, Countdown is iconic British TV. Its numbers game is the perfect balance of challenge and simplicity. In this video, I analyse the hidden mathematics of the game: What are the hardest targets, best numbers to draw, and optimal tactics?
⬣ TIMESTAMPS ⬣
00:00 - Introduction
04:46 - How Many Possible Games?
10:00 - Reachable Numbers from a Given Game Set
14:00 - Results and Tactics: Small Numbers
24:00 - Results and Tactics: Large Numbers
31:00 - Scary Numbers
40:05 - Outro
⬣ CHALLENGE ⬣
So to clarify, I want to see a list of the percentage of solvable games for ALL options of large numbers. Like I did for the 15 options of the form {n, n+25, n+50, n+75}, but for all of them. The options for large numbers should be four distinct numbers in the range from 11 to 100. As I said there are 2,555,190 such options so this will require a clever bit of code, but I think it’s possible! Email me via my website if you think you have it!
⬣ FILES ⬣
drive.google.com/drive/folder...
⬣ INVESTIGATORS ⬣
I’ve never seen that colour on my screen before. I’m hoping you excel yourself and slug out the solution. Now is the perfect time to join the investigation.
⬣ REFERENCES ⬣
wiki.apterous.org/CECIL
Blog I mention which uses reverse Polish notation:
datagenetics.com/blog/august3...
⬣ CREDITS ⬣
All music by Danjel Zambo.
Images
Rachel Riley: commons.wikimedia.org/wiki/Fi...
Carol Vorderman: upload.wikimedia.org/wikipedi...
Teapot: upload.wikimedia.org/wikipedi...
Cecil Korer: wiki.apterous.org/images/c/c5...
OK Emoji: upload.wikimedia.org/wikipedi...
B Footage
8 Out of 10 Cats Does Countdown, Countdown © Channel 4.
The Chase © ITV.
Have I Got News for You, Only Connect, Pointless, Richard Osman’s House of Games, University Challenge, The Weakest Link, Would I Lie to You? © BBC.
Des Chiffres et Des Lettres © France 3. - Zábava
CORRECTIONS AND CLARIFICATIONS AND CHALLENGE UPDATE
1. I've seen many comments challenging my method at around 13:20 by saying that numbers greater than 1000 are allowed because we might then divide or subtract to bring them into the 100-999 range. I never say otherwise, but I think my explanation was unclear and I apologise for that. I don't exclude the possibility of generating numbers greater than 1000, just that the only numbers we store are the ones that land in the 100-999 range. For example, if we generate 1500 during calculation, then we continue calculating with it (because we could for example later divide it by 2 to obtain 750) but we don't store 1500 in the solution set, we only store 750 in this case. Hope that clears up that point and sorry if it was unclear!
2. Huge thank you to viewer Trillian who spotted an issue with part of my code. I mention that I sort the set into descending order before applying the various operations. For the section on the "scary" numbers (31:00 onwards), the first operation was performed on an unsorted set, so a very small amount of solutions were missed. It's a minor fault and I believe the conclusions will be the same, but I'm running it again to be sure.
3. Pretty sure viewer Trillian has solved the Countdown challenge. Can't wait to share the results with you in a future video!
*Is Countdown Britain’s oldest game show? Strictly speaking, “A Question of Sport” and “Mastermind” have aired for longer; similarly for University Challenge though the modern iteration has only aired since 1994. However, when writing, I categorised these as “quiz shows” as opposed to "game shows" as they are almost entirely based on trivia and knowledge. Countdown isn’t a “quiz” since the contestants aren’t answering trivia questions but are competing in a game. All of these shows are categorised as “game shows” in the world of TV production so you have reasonable grounds to disagree with my classification. Personally, I like the distinction between quiz and game. And also it makes for a snappy title.
**On the notation “nCr” for the “choose” function. This isn’t my preferred notation, either. But all other options use superscripts, subscripts, or don’t fit on one line. All the other options reduced the readability, especially in some of the busier diagrams in the video, so I went with the less-standard but ultimately neater option.
Question of Sport IMHO is a celebrity panel show, not a game show or quiz show - it’s mainly about vaguely famous people being entertaining, not actually winning the quiz.
Excited for the video!
Sorry, you didn’t specify TV. Just a Minute is a panel game (which is a form of game show, see both Wikipedia and BBC descriptions for confirmation) which has run from first airing on 22 Dec 1968. And I’m Sorry I Haven’t a Clue has run from Apr 1973. Neither are quizzes. These are both considerably older British game shows than Countdown.
Why do you call 10C4 “ten choose four”? When I was learning probability and statistics, this was one of two calculations known as permutations (P) and combinations (C). What do you call 10P4?
@@langdalepaul Hello, I think that is the common way of saying that aloud! I don't think there's a specific way to say the permutation one
Thanks for clarifying, because I also misinterpreted your meaning regarding numbers bigger than 999.
Looking forward to your Numberwang episode.
People that know these reference are probably older than current Gen Z lel.
Also, 5.
Let’s rotate the board!
Das ist numberwang!
Twentington?
Shinty six
I just remember that one time where the target number came up, and Rachel instinctively said “Oh dear!” immediately, because it was impossible.
I remember a 8 out of 10 cats version where no one got it and Rachel thought there was no way to do it but didn't seem sure of that. I paused and worked on it for 10 minutes or so because it looked doable but could find no way either.
@@wingracer1614 There was one where Rachel wasn't sure but an audience member had it.
I remember one carol couldn’t get but a child from the audience did
@@wingracer1614 Rachel also will re-roll on cats does countdown every once in a while if she doesn't like the number. She re-rolled 666 on one episode. Not sure if she does the same on the main show.
@@Dan-uh9sg No, she definitely never does it on the main show, they have to keep it RNG for fairness. They do it on cats because nobody’s there to win anything, it’s just comedians mucking about. The 666 one might be that time they were betting on who could guess closest to the next generated number
8 out of 10 Cats Does Countdown is possibly Britain's greatest gift to the world. A silly yet sublime conjunction of comedy and skill.
It's so much better than the original 8 out of 10 Cats as well. It shouldn't work, and yet it's just magic.
I don't know why they don't jusf make 8oo10 the main show 🤷🏻♂️🤷🏻♂️🤷🏻♂️
at least have Jimmy be the host of both
"skill"
Sean Locke and Aisling Bea are my absolute faves.
@@Anzuo Of course it is skill. Haven't you seen all the acrobatics Jimmy does? ~especially with taxes numbers~
.
Just because people on the internet can't really understand sarcasm: I know that when jimmy "does" thoese acrobatic bits and etc, it's not him.
Richard Ayoade using a 3 & 2 to cube and then square respectively, is some of the best TV ever
If you wanna square and cube things, get a job in a fucking jelly factory, mate.
The fact that he didn't get points gor that is the worst thing that ever happened in British television
I was unaware of the limitations of the operations allowed until that episode, as I'd solved a few by squaring numbers, and was always curious why no one else ever did.
@@kami3000 The only one I've seen with him in he definitely won, got a 9 letter word (tnetennba).
@@kami3000 Fair enough, but 8 out of 10 Cats Countdown is a comedy gameshow after all, and it is (as far as I am concerned) considerably more entertaining than the standard version where they seem to take anagrams and arithmetic far too seriously!
Your request for improved code has sniffs of Matt Parker's wordle code recently. That got into milliseconds from an original couple of hours. Expect improvements!
You are downplaying it massively. They got it down to ~300 microseconds from Matts original code, which took ~1 Month
Exactly was i was coming to comment! There will definitely be a solution to the full problem soon.
As they often say, the best way to get a correct answer is to post something slightly wrong on the internet... Millions of coders rushing to make the best version as we speak
An evening with a few beers and dusting off my knowledge of C, and I got a program running in about 35 minutes. Not as great as the 90 seconds some others post, but not bad either I'd say.
I got it down to about 1 minute, still too slow. I ran out of tricks.
As noted elsewhere, it is called Letters & Numbers in Australia. In a very Aussie habit, the contestants started giving the number combinations nicknames. Two large & 4 small numbers were the Family Pack. One Large and 5 small numbers were the Single Parent. The 4 large and 2 small were the Heavyweight and the notorious 6 small numbers were called the Rat Pack. I can't remember what 3 large and 3 small numbers were called.
That's so Aussie, and I love it.
Sounds like Bingo callers branching out.
@@claireongley7724, My apologies about the 5 large/1 small - now amended to the heavy weight as 4 large & 2 small. Thanks for remembering the Perfect match.
I only know two large as the Sean Special.
@@AnotherRoof our version of Top Of The Pops was called Countdown. Although it hasn't been on TV for over 20 years, enough people remember it, hence the name change
I was on Countdown 20 years ago and asked Carol if she used factorization, and she said she normally just aimed near the target, and adjusted as necessary - the "pitch and putt" approach, I guess. People might be interested (or even surprised) to know that if the target is 999, you can get it with 1 1 4 6 6 7...
Now this interests me. From watching older and current episodes, you could tell Carol was most happy when the contestant picked one large, but Rachel is always nudging the contestant to go for the more challenging six small or four large.
I have certainly noticed that Rachel likes factors, and Carol didn't quite so much.
Though I think I do recall on one occasion Carol saying that 27×37 = 999.
Congratulations on making it on the show and thanks for watching!
@AnotherRoof i have one complaint about the show why show a full cock and only use half of it?
How did you get on and how many episodes did you manage?
I think there's a more obvious reason why 7 and 9 perform so well. Odd numbers allow you to change the odd/even property of your total by addition and subtraction, and even numbers do not. Even numbers multiplied by anything are even. So odd numbers can probably access more target numbers by making it easier to flip between odd and even, or preserve oddness under multiplication.
Could always divide an even number by another even to get you the odd.
@@Deifiable
Only works with some even numbers, and uses 2 numbers
As an American, I discovered British panel and game shows through QI and since then I have completely fallen in love with them. Would I Lie To You and QI being my two favorites, but I have at least watched most of them.
The world of these shows is vast and with a recurring cast of comedians, all with the kind of quiet grace of British TV which is so, so much better than the loud and drama-filled US TV.
If I had been born in the UK, I imagine I would completely and totally agree with you about how strongly I identify with these shows.
Yeah. We usually hate US adaptations due to them being over the top. That and constant background music throughout (although most people may not realise it).
British versions of many American game shows have gone under the radar for many reasons. The British version of $64K Question was hamstrung by legal and budget constraints, the British version of Jeopardy was restricted by the amount of money you could give away in those days, the original UK version of Pyramid was no fun even though it was hosted by a very competent presenter in Steve Jones, and a bucketful of others.
@@bobomb1986 Jeopardy is the one US gameshow that I think is on the same level as UK gameshows because it has the quiet grace I was referring to. Although, I haven't seen it since Alex Trebek passed, hopefully it hasn't changed too much.
@@Scum42 Just going by what my American friends have said, I think they do like what Jennings brings to the show.
where did you watch a lot of these shows? i want to try watching a lot of them myself in America
I love watching 8 Out of 10 Cats Does Countdown. Especially Jon Richardson v. Sean Lock (RIP, 2-time Carrot in a Box Champion). Their chemistry is absolutely incredible. What are your favorite team captains/players?
I love the fact that Jon unabashedly takes the game seriously, despite being on the parody version.
A player I struggled with a lot was Roisin because surely no one could be so oblivious. But over time I've come to like her more because she is. Although part of that is because she has also become a better (not good, no where near good) player and takes more interest in what's going on with the game.
Some of the guests they bring into dictionary corner though are just so vomit inducing. I can only think they keep getting called back is because they are so disliked it generates publicity or they have an in with the producers.
@@qwertyTRiG you can honestly tell he's quite perturbed by his minor celebrity as he can't go on the regular one anymore!
Crying at “2 time carrot in a box champion” 😂😂
@@Paldasanit is the spot which allows for exposure of less favourable or less familiar comedians, veer off course and play around with the format. I have a few cringe worthy visitors but most I really enjoy exactly for the reason stated above
"Remain Indoors" that's brilliant and also that's Numberwang!
37 on the thumbnail. Veritasium video broke me
as a non-brit that's really gotten into British TV recently, this entire episode and especially that "REMAIN INDOORS" was very much welcome.
"YES"😬
Being French myself I have to set the record straight. The French game « Des chiffres et des lettres (numbers and letters) » is actually a merger of two older games, « le mot le plus long » (the longest word) and « le compte est bon » (countdown). Or so I thought. I don’t know the old formats as they merged long before I was born. According to Wikipedia « le mot le plus long » was renamed « des chiffres et des lettres » following the addition of the countdown part.
You interesting French person, you.
Yes, very popular French game and it's been around for longer than this British show. But then, he mentions that in the video, right?
"We would also go through another two mathematicians." Brilliant!
I wish this had been around before I was on Countdown :D
The only real preparation I did before going on was I decided to consistently choose three large and three small, which is still a relatively unusual choice.
Choosing 1, 2 or 4 is more common overall, and that was one of the reasons I went with three, my opponents were immediately wrong-footed by it. Additionally, I noticed that a lot of players forget that they can use two large numbers to create a small, so I tended to treat three large and three small as one large and four small (in effect), selecting the most utilisable large number for the "pitch" and then using the other two as a small number in disguise :D
On one occasion, n the semi-final, I had to do hat in reverse, using two sevens to get close to 50 and then multiply that up to the target number, unfortunately I overthought it and ran out of time before completing the solution (which would've got me five points, IIRC).
I was once a contract programmer for Channel 4, and they used Java for some of their back-end. To practise it, since I wasn't overly familiar with the language, I decided to develop a Countdown numbers game solver, because hey, it's Channel 4! You select your 6 numbers and target and used a brute force approach using Reverse Polish Notation, since it translates well into programming via a stack. I actually used the "famous numbers game" of 25 50 75 100 6 3 with a target of 952 as a test case, and it came up with quite a few interesting results, such as making 927 first (which is convenient as it's a multiple of 3) then adding 25 at the end (in this case, the solutions tended to be permutations of either making 927 and adding 25, or making 23,800 and dividing by 25).
I hope you gave your program a name like they did for CECIL...
@@AnotherRoof Unfortunately I didn't. I should have done!
That is amazing! Thanks for sharing your expertise and insight.
I might have played your game as a child.
I think it’s also worth noting the time limit and the sheer familiarity contestants have with the traditional set of large numbers when considering what makes a set of large numbers “challenging”. Like you said, you can always divide by 25 in the original set to get a 2 or 3, but that’s not possible in any other set. Those rules of thumb go out the window when returning contestants are faced with new sets of large numbers.
It’s also generally more tricky to multiply something by 19 or 64 on the fly than by 25, 50, or 100. I think that’s also why that guy couldn’t figure out what his partial solve would be when he multiplied it by 75 on the fly. Most people generally can’t rely on rules of thumb for multiplying three-digit partial solves by large numbers other than 25, 50, or 100. Doing all that comparatively complicated arithmetic in 30 seconds would, indeed, challenge the champions, I think.
Exactly. Most people will end up breaking the large numbers down into a familiar large number (Ending in 5 or 0) and a small number, so 63 becomes 60 and 3, but this doubles the number of simple calculations you are doing in your head. Those calculations really add up, especially with more than one large number.
The guy could have done the calculation quite easily starting from the end if he'd had a bit longer to think about it - divide his target number by 4 and mutliply by 100! (then add 50)
The fact that countdown has been going on for 41 years (at the time of the video) and the video just so happens to be 41 minutes long is awesome
Numberwang-adjacent reference earned my subscription. Well done, sir.
The theme tune to Countdown was written by, amongst others, Brian Bennett who also played on the recording. The source of this information was from Brian himself when he appeared on 'Face to Face' with Rick Wakeman (it's on You Tube).
For those who don't know who Brian Bennett is, he replaced Tony Meehan in October 1961as the drummer of The Shadows.
Oh I'm so hyped for this, always have been intrigued by this game and also other similar arithmetic number puzzles like 24 or the Four 4s and I haven't seen a ton of exploration from them so this is cool to see
Honestly, it's completely unsurprising that the multiples of 25 are the worst performing set of large numbers, there is a lot of redundancy in that set.
That said, there is a massive difference between "possible for a computer to do" and "easy for a human to do in 30 seconds".
Humans will naturally tend to favour numbers that are essentially 1/4, 1/2 and 3/4 times 100 from simple familiarity, particularly when speed is of the essence. Obviously, it's possible to learn your 79 times table but it's trickier (at least for mere humans).
Was about to say the same, the challenge isn't so much the ability to reach a solution but rather to reach a solution within the time frame.
@@johnpotts8308 I think if you know the numbers before hand it really shouldn't be that hard to learn your time table up to 10 for all 4 of them and become just as familiar. For casuals? No doubt 25 etc is the best because you know them but if you know the numbers and have prep time you should be able to become as familiar
@@johnpotts8308 but that is not a thing to worry... work your 8x table and use 79=(80-1)=(8x10-1)
6 x 79 = 6x8, add a zero, subtract 6
48 => 480 => 474
being able to split/complete numbers and use distributive property is precisely the reason times table are only considered up to 9
after that, start spliting/completing and making numbers easier ^_^
@@RadeticDaniel I myself usually have the 25s, 50s, 75s and 100s memorised, so can easily work out my 79s as being the 75s plus the 4s. Although I did mix up two numbers in the 75 times table once, which was a little embarrasing for me.
reverse polish notation is what I thought of immediately for finding the solution spaces so I'm glad it was mentioned at the end
Yeah, this kind of thing is really the only use for Reverse Polish notation now that pocket calculators (or more realistically, mobile phones) can handle parentheses.
@@ShankarSivarajan It can be useful to precompute equations that will be run very frequently into RPN in programming too. Especially for more complex function strings setting up an array in RPN format using pointers to the input values rather than parsing the string into something useful every cycle can be better. Doesn't really help much if you are only executing the equation once but if you are going to execute the input equation on a large dataset it is quicker. That just being because string parsing is way more expensive by far than the arithmetic operations themselves so if you can avoid redundancy in doing the former it will help significantly. It would make it a lot quicker for example if a program was told to run the typed equation a*(b+c)/d on a binary file containing 1,000,000 sets of 4 integers, the string parse would take way more operations than loading those bytes and iterating over a precomputed array of pointers and CPU opcodes in RPN format that had the same effect as that equation.
Thought about it a bunch, and I can't see the advantage of RPN in this context
When I was doing my first year studying Maths in university, one of our modules, the statistics one, had a piece of coursework where we had to use what we'd learned up to that point to analysis a probability distribution of our choice. Some examples of ones we could use were given, which most people used, but I went and did an analysis on how many different Numbers rounds could be made for Countdown. Because it was just an analysis of the probabilities of each set if numbers and not if any were possible, I didn't go too far, but I had been told that if I'd wanted to do a further analysis for a dissertation in my third year, then a few of the lecturers would have interest in working on it with me. Didn't end up doing that, but it was something I wished I had done.
EDIT: Because I did my coursework on a notepad that exportedd what I wrote digitally, I was able to find what I did in the cloud and checked my numbers with what you had in the possible games portion of this video and had the same as you, aside from the bit at the end where I multiplied 13,243 by 899, due to 100 not really being a possible target in the main show. This meant I had 11,905,457 total possible games.
The intuitive explaination behind why 1 and pairs of small numbers don't achieve many results really tickled my brain, really elegant and, well, intuitive interpretation.
Thanks so much for this! Always when I watch countdown I wonder these things but then forget to look into them! You've cured me!
Recently went down the rabbit hole of 8/10 cats does Countdown (I'll let you guess why). So much more fun and thought provoking than the trivia shows I grew up with. Thanks for the awesome explanation to all my questions I didn't know I had!
"I'll let you guess why" Was it the knob gags? 😂
I'm not into maths at all, but this was an accessible, interesting and engaging video. Subscribed!
Great video! I think there is also an important non-mathemaitcal reason for choosing the big numbers, which is - human intuition (or at least, decimal-based culture raised human's intuition). Though there are more sollutions with n=19, as shown in the video - we think in 5s and 10s. And by "we" I mean both contestants at the studio and viewers at home, who need to follow the game and feel it is relatable for them.
The University Challenge clip you used was from the season I was on. I played against that SOAS team, they were excellent!
As both a fan of Countdown and a mathematician, I really enjoyed this video! Great content and it was a super interesting watch! You have a new subscriber!
Thank you SO much for this. I’ve finally realise why the Australian version is called “Letters and Numbers”, rather than the more famous “Countdown”.
If you’re going to license a show, you might as well only pay one rights holder (ie French), rather than paying two (French and British) when the second one is just a name.
Also in Australia there was a music based show called Countdown.
they definitely did it because of australian countdown (the music show), it would have been too confusing otherwise. although it being cheaper I'm sure helped!
Countdown is a tv show as well
Same in Spain, it was called "cifras y letras" (numbers and letters).
@@James_taylor810 ...and it was great! Check out Molly Meldrum interviewing King Charles the third on Countdown, it was most amusing!
Hyped for the video! Your content has been nicely evolving
For this video, I even moved my chair to the left side of my desk instead of the centre, a first for the channel!
@@AnotherRoof a master of your craft 👏
Your editing keeps getting better, love watching ur videos :D
First time on this channel and what an excellent video! I have long thought about analysing Countdown but you have excelled with your approaches. Fantastic :D *subscribed*
I can't believe you explained that famous numbers round (@29:16) and now I completely understand how he did it. It just takes some mathemagic, and you look like a genius.👌
I live in the US. I went to the UK in vacation in 2015. My British friend introduced me to Countdown and 8 out of 10 Cats does Countdown. I still watch 8 out of 10 and discovered several dozen panel shows hosted by comedians and then all of them guest on the others shows. I also have the Countdown clock on my phone.
This was a LOVELY video!! Sure I enjoyed the math breakdown, but you are SO adorably British, and I learned so much about y'all's culture from this video!! Keep up the great work, mate!!
I've only seen two videos of this channel and I already love it ! I should go on an Investigation to find other channels like these... To Focus on a subject and give intuition about it is the best way to learn !
This game has existed in France since 1972.
One of the winners of multiple shows in 1975 became one of the show co-hosts and stayed until... 2022!
I think the French version of Countdown been going since 1965?
@@ruairi_d I think before 1972 it was just the letters but I'm not sure
@@ruairi_d up until 1972 there were no number rounds and the show was still called "the longest word."
@@bjoern.gumboldt ahhh that's cool. Didn't know that!
I was watching it around 1990 on TV5, even though I didn't speak French!
In Spain, there was a similar show, also based on the french one, called Cifras y Letras. It ran between 1991 and 2012.
loving this way of visulisation. explains way better than my thought process. i thank you
I appreciate the effort this video took, and loved it. Thanks!!
One concern I have with your calculations is the difference between total count of sets and the probability of each set. I'm not sure if it's accounted for somewhere (maybe combinations vs permutations?) and I missed it, but a set like 100 75 50 25 2 1 is much more likely than 100 75 50 25 1 1, as the 2 1 can be drawn as 2 1 or 1 2, which is drawn at a 2.1% likelyhood, where 1 1 is drawn at a 0.05% likelyhood. in this case with 4 large numbers, any duplicate occurs 5.2% of the time (1/19), which is FAR lower than the expected 10% found using simple permutations.
You are in my top 20 of all youtubers and 4 in math. Mathologer, 3b1b, and numberphile in the top 3. And numberphile is swingy based on guest. You are better then many of his guests but some guest top even Mathologer.
I get excited every time you drop a video. Please keep it up.
For reference, I actively watch 483 channels.
That's so cool? Do you keep up your watching stats or something?
Did you rank all the youtubers you watched...?
But out of curiosity, what are your top 20 or such favorite channels in general ? could be interesting to learn about :D
Add one more and make it a perfect square.
Number OCD strikes again ...
This Investigation into the mathematics behind the Countdown game is beautifully done! I must say the production quality of your videos is extraordinary - supernatural, even...
What a great find your channel is for me. I recently searched CZcams for videos of the show Countdown, so the algorithm put this video on my start page. Sometimes the algorithm isn't so bad...
90 minutes for one set of numbers? Well, if we get some of Matt Parker’s viewers to tackle the problem, they should be able to come up with a program that runs in a few milliseconds, considering how they solved a problem he needed a whole month for in less than a second. Simply switching to a different language (or maybe even just using pypy) would probably give a speedup of 10 to 100 times.
I got a brute-force solution for a given set down to 2.2 seconds using a RTX 4080 GPU. But going through all 2.5 million combinations would still take about 60 days! So more clever approach is still needed, which re-uses previously found results.
Nice vid. I actually would have done 20 choose n for my small nos, because that's weighting the sets by their probability of coming up, which is what you care about as a player.
Yeah this is a really good point from a gameplay perspective! But in a "total possible" perspective I didn't find a simpler way of counting them!
I can't believe I had to scroll to here to see this. I was screaming by 8:13... It's 20C4!!!!
What a great video, I got lost when you started talking about champion of champions numbers but other than that I was hooked
Excellent video! Fun to watch and interesting
The universally acknowledged Matt-Parker's-Law of "I'm just a mathematician" programming challenge clearly states: for every Python script whose runtime is over a minute, there exists a C programmer, whose sub-millisecond solution is hard to be measured precisely.
I have both a degree in Applied Mathematics, and Computer Science.
But couldn't be bothered to solve your ending conundrum without being able to win a teapot!
21:58 - Some slick editing - the 6x4 inside the parentheses magically corrects itself to 6x5 as the blackboard is placed away from view behind the counter. Play it in slo-mo and you'll see what I mean.
Anyway, the content is superb, and I learned a huge amount. Many thanks for uploading. Please take care and stay safe.
Remain Indoors! You are now my favourite mathematical youtuber. We don't talk about the event! Mitchell and Webb were my childhood!
mind blown. I love University Challenge, I spent a few months watching a lot of TV and Quiz night on BBC2 was something I always looked forward to. Whenever the camera pans to the team conferring, I always imagine them saying "Venezuela Venezuela" to each other, I think it was in a sketch show from some point in the last 30 years where on team just continually gives Venezuela as the answer. I'm just made up that somebody actually did it on TV
The sketch you're thinking of is from Armando Iannucci's Time Trumpet: czcams.com/video/QKQ29aR3uK4/video.html
@@Pointland33 that was Tesco vs Denmark, but I see your point thanks. In 1983, no one died, in 1984 no one died, in 1985 no one died, in 1986 someone died... In 1987 no one died.
REMAIN INDOORS
Brilliant! I chowed down on my protein fudge as soon as I saw that.
I have a sudden urge to rewatch that episode of IT Crowd hehe
Thanks, awesome video!
Great job on explaining the game, as for your code. I love it .. thank you so much
I love Pointless in particular; the fact that zero points is the best, it requires Pointless trivial knowledge and the presenter and dynamics. Also love eggheads, university challenge and QI. You have a productive country in terms of quizzes and game shows 🤣
University challenge is great because when you get a question and the anoraks on the panel don't, you feel *really* smart. Even when it's a category like shoujo manga or pop music that the poor nerds had no hope with.
The funniest thing about Pointless is the celebrity version which is appropriately called Pointless Celebrities because all the celebrities really are pointless!
Loved the explanation (in Aus I think we derive the French name for the show - "Letter and Numbers") (and I spotted the edit for the 452 example around 22:00 :P )
Really great presentation and a very informative video!
Another thing to take into account with the large numbers change is the time limit, although mathematically it maybe that the numbers are technically better, those nice round numbers are much simpler to work out quickly for most people.
"Upon solving a problem, you realize you weren't the first person to do it."
Was it Euler again?
Ha! Probably not this time. Although I wouldn't be surprised.
It always him.
The trouble with Euler is, people start using his name even for things he didn’t invent. Like “Euler operators” for mesh construction in computer graphics -- he had nothing to do with those.
Great video, have watched countdown since I was little.
The perfect amount of nerd + maths = genius content ❤
1:41 - yeah, I'm with you on this. UK game shows (or panel shows) got me throught covid lock-down
I've got it down to ~90 seconds per deck (100 75 50 25, etc) with C# and Multithreading... I'm sure there are some other ways to improve it but that's where I'm at for now. Pretty much just implemented exactly what you talked about. I considered RPN for awhile as I'm well versed, but I can't see how it would help, and any memoization seems fruitless too since it's usually quicker for the CPU to just do the 5 math operations rather than look up a value amongst billions of others... But I'll think on it some more! I also used the fact that all the smalls can account for 2850 of the 13243 gamesets, so I never have to calculate those again.
A game deck consisting of the cards: {14 13 12 11 } can hit every target exactly 857/13243 times (6.47%)
I have not watch the whole video yet, but to consider the number of possible combinations of scoring numbers, I segment this by number of pairs.
There are 10C3 = 120 ways of having 3 pairs of numbers (all small).
There are 10C2 = 45 choices for 2 pairs, and 12C2 = 66 choices for the other 2 singles 45*66 = 2970.
There are 10 choices for 1 pair, and 13C4 = 715. 715*10=7150.
Finally there are 14C6 = 3003 possibilities for 6 unique numbers.
So in total we have 120 + 2970 + 7150 + 3003 = 13243. Though this was done quickly, and may contain a mistake.
There is also the combinatorial inclusion/exclusion principle.
There are 24C6 = 134596 combinations of tiles that can be chosen.
However, this double counts sets with one single small number, quad-counts those with 2 single small numbers, oct-counts those with 3 etc, 2^n- counts those with n.
The inclusion/exclusion principle tells us the total number of sets =
#combinations of tiles - #duplicated tiles × #combintions from the rest + #dupsC2 × # combinations of rest ...
Please note the alternating sign.
Here we would have
24C6 - 10×22C5 + 10C2×20C4 - 10C3×18C3 + 10C4×16C2 - 10C5×14C1 + 10C6
Each term represents the number of ways of choosing n number to be singles, multiplies by the number of ways of choosing 6-n from the other 24-2n tiles.
This gives 134596 - 263340 + 218025 - 97920 + 25200 - 3528 + 210 = 13243.
Fun fact, the guy at 29:07 (James Martin) was my maths tutor at uni; he was so modest about it but you could tell how proud he was deep down that this achievement went viral and he became some recognised for it
Excellent video and explanations. Thanks!
I would think part of the challenge with those scary numbers would be how uncommon it is for someone to work with those numbers. People are quite comfortable with working with multiples of 5, 25, and 100 all the time. When was the last time someone asked you to do something with a 37, especially with the pressure of going against a clock. So regardless of whether those "weird" numbers would help or hinder the contestants, at least from the audience's perspective it would seem more challenging.
Fascinating video!!
B28 I34 F30
But what does the code mean?
@@tomaspecl1082 it was G28 I34 F30
@@andrewewart7166 yea but I still dont get what it means. Is it a reference to something? Or is it a cipher? What is the purpose of it?
Enjoyed it, thank you. My mum was on Countdown in the 80's.
He stayed so calm through this! I was getting stressed trying to figure out how 3,3,2,2,1 and 1, could sum up to 81.
(3*(2+1))*(3*(2+1))=81
Excellent video! I regularly play the game on my phone, and being in France I knew about its origins (the original creator is named Armand Jamot FWIW).
One thing though: in the rules you also have the fact that any result from any operation must be a strictly positive integer, AND the minimum number to achieve in the French rules is 101, not 100.
I am Italian and I also love TV quiz shows. In the 1980s we had our own version of Countdown: it was called "Paroliamo."
In this show, there was the game with the numbers that was showed in the video and it was called "Contiamo" ("Let's Count").
I remember being a child and trying to do the math operations with paper, pen and calculator to make it faster!
as a canadian, i'm surprised there is no north american countdown. i've always loved countdown. great game :)
It's mildly surprising there's no Canadian version, but surely it's obvious why we've never had a version here in the states. :^/
So I don’t have an answer for the challenge (yet at least) but I did recently code a program which can solve combinations with limited repetition, which would make counting the number of possible games easier. I also came up with a formula involving repeated sums, but my code, thankfully, does it a lot more efficiently than that. I found it was a problem which I was facing pretty regularly and so I made a program which can take in any number of objects and specify how many repeated objects of each type are allowed and spits out the number of combinations. I don’t want to explain my whole thought process and intuition of how I made it if no one’s interested, but if anyone is, let me know and I’d be happy to! Good luck to anyone tackling the challenge!
Interested!
@@captaindapper5020 Haha, thanks, that means a lot to me! So I’ve just recently gotten into coding so there’s definitely a far better way to do this out there somewhere, but what I did was systematically count up through every possible combination of choices across all the groups using the number of items in each group like a digit in a weird multi-base type number (so say I have 3 groups of 2 objects, starting with 000 then counting up to 001, 002, and then 010, but it works with any number of groups with any number of varying amounts of items in each group). For each one of those combinations whose digits sum to the number of objects being chosen, I add one to a counter which spits out the result after counting through. You can also do permutations similarly by multiplying the result by several different regular standard-issue combinations.
I love the maths round of Countdown, and my favourite game set to work with is 3 large 2 small. [Apparently, The hardest game set] but your breakdown of this game has given me a better understanding of its system. Thank you.
How can you only have 5? Or do you mean you choose six but ignore the last number? Or pick which number to discard?
amazing analysis. Who ever knew this was what was going on in my head when I solved most of the numbers games before the clock expired...
13:30 I hope I understand correctly that you put the number into the solution set if it is in {100,...,999}, but still continued the process with it, since you can go well above 999 and still come back down to the acceptable range with division and subtraction
That's common when you want to do things like x3 and -2 to get the answer, e.g. by x75 first, then -50, then /25. You are sharing the 25 between the 75/25 and 50/25 parts. A number of contestants have used that strategy in the series.
You should try for a collab with Matt Parker. He has done similar types of videos for other numbers problems. He would love this
Loved the Mitchell and Webb reference as well!
I love how just that rhythm of the last few seconds of countdown music can be tapped on a table and it has its own meaning. It gets used a lot when playing scrabble in our home...
The best way to chose your set of numbers is always 4 little and 2 big.. just as Sean would have wanted.
Rest in Power, Sean. Forever a cheeky bastard. ❤
Why only 5?
2 big and 4 small, the Sean Lock Special, or the Usual.
@@SennaAugustus yup, mistake, I don't know how I accomplished that, as I do remember thinking two, but typing too, and corrected for that, but got one?! I'm not sure, but I'll just be like Johnny and sheepishly laugh at myself. 😊
Fantastic video, while your on a roll I was wondering if you could explain the other big British number game; Numberwang!
As a newcomer to the show I've struggled to reliably guess what is and is not Numberwang! and I'd love to hear your thoughts on how to improve ones Numberwang!ery.
It's easy. If a number named by a contestant is in fact Numberwang, then it is declared as "Numberwang" by the host and that contestant may or may not score points.
I believe there is a mapping between the positive integers and finite sequences of London underground stations, such that Numberwang can actually be considered a variant of Mornington Crescent.
Basically, it's a Numberwang if it's the inverse coefficient of a Wanganum.
I loved this show so much, but alas, being across the pond without cable, I haven't seen it for years. Thanks for tackling it here.
4:00 Jimi hanging off the telephone wire and a shirtless telephone repair-man is what those seconds bring to my mind, IDK what your talking about xDDDDDD
definitely appreciated the Mitchell and webb reference
Ha, I came here to say this exact phrase!
I think uneven numbers make sense, because you can get to an even number easily with uneven numbers, but it's much harder to get to an uneven number with even numbers.
Looks like the puzzle nytimes is doing a beta for, digits! Cool to find a video that already covering stuff I just learned about! Worried this will mess with my own process too much right now so gonna wait on watching until I feel like I'm no longer having fun coming up with new strategies.
Comedians furiously studying this video before appearing as a guest
Holy shit I got the university challenge question right about Eigen values. That was deep storage knowledge awaked from the depths from when I was a game dev student in uni. I've never had cause to use that knowledge in my life.
I was really surprised by one episode where the target was unobtainable. For many years I thought CECIL was choosing some random series of operations on the given numbers that would lead to a number from 100 to 999. But it turns out it's just a random number generator, and the number of possible targets for most sets is so big that it usually just works out anyway!
Not sure that Cecil is completely random as it doesn’t often pick a target that is fairly obvious for the given set.. would be boring telly if it did.. would love to know more about how Cecil picks the targets?
@@RobertFranksPlus It's just a random number generator. It will generate "100" sometimes when there's a 100 up there, lol.
@@RobertFranksPlus There are outtakes out there where CECIL just throws up obvious numbers. Usually, what they'd do on the show is just cut it out and roll a new target.
RE: The point around 37:00 regarding Scary Numbers. Something I would have looked at is how divisible the large numbers are by each other. Given that a big part of the 'Pro Strat' seemed to rely upon the fact that [100/25 = 4; 75/25 = 3; 50/25 = 2]. The Countdown challenge is, crucially, a timed one. The difficulty doesn't revolve around a solution being possible; but a solution being divineable in 30 seconds.
So relieving the Competitors of one of their chief tools would seem to have quite the effect.
I watch all of those game shows. I watch Richard Osman's house of games for fun and only connect when I'm feeling too smart because I can't get any of it. From the us but travel to the UK a few hours pretty much every night. Thanks for the cool video
I'm not a programmer, but for the random set of large numbers I'd extend your idea:
If you have calculated the reachable targets for 11, 12 and four smalls, you can add that to any set of large numbers that contains 11 and 12.
Similar for three large and three smalls, and four large and two smalls.
Interesting that a British institution such as Countdown was imported from France.
Yes, as were half the words in your sentence: interesting, institution, the ‘count’ part of countdown, and imported. 😉
A long tradition of shared history… 🌹🐓
@@TheDibule ah yes, the ultimate symbols of sharing: roses and cocks.
A complete nutter. An utterly unnecessarily deep analysis of a parlour game for no reason at all. A perfect example of how a mathematician thinks, if you want to call it that. A great video!