The Surprising Maths of Britain's Oldest* Game Show -

The Surprising Maths of Britain’s Oldest* Game Show

Another Roof
Views: 619576
Like: 9897

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?

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

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!


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.


Blog I mention which uses reverse Polish notation:

All music by Danjel Zambo.

Rachel Riley:
Carol Vorderman:
Cecil Korer:
OK Emoji:

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.


  1. 38:50 Classic just chuck already found solutions in a cache to make code run faster. Love it.

  2. We don't talk about The Event. Remain Indoors.

  3. Bring back the Krypton Factor! That was a quiz show that really tested people, if perhaps a bit elite, but then I guess that was the idea of the game.

  4. Countdown is copied from Des chiffres et des lettres

  5. I think for the final challenge, I'd have said picking one number from 11-25, one from 26-50, one from 51-75 and one from 76-100. This way you still get a spread of high numbers, and excludes sets with 51, 52, 53, and 55 as the high options. But really interesting watch. I guess computing power has come far enough we can force these questions now.

  6. Add the 1's to 2's
    3 3 3 3
    81 is highest I found for 112233

  7. I'm from the US, and Cats Does Countdown is my favorite version of the game. 😁🐱

  8. Is this why I was in love with 7of9 from Star Trek?

  9. The spanish version has going on and off for a while and it's coming back at the end of 2023.

  10. nahhh, countdown and pointless are both on the abc network and me and my family love those shows

  11. For me it seemed easiest to deal with multiple of 25 for the target of 452… I did ((4+5+9)×25)+(7-6)

  12. Remain Indoors! You are now my favourite mathematical youtuber. We don't talk about the event! Mitchell and Webb were my childhood!

  13. There is one more calculation – the case where the target is 100 and 100 is one of your number set (although I suppose we already know that this is an approximate method since some will be illegal combinations). Interesting video!

  14. my bad for thinking i would like this video 👎👎

  15. Countdown is also known as "Letters and Numbers" in Australia. I don't know if it's because they're trying to keep true to the original French name, or to avoid it being confused with a popular show from the 70s and 80s ("Countrdown" was basically Australia's version of Top of the Pops).

  16. I share your love for game shows. I haven't seen the proper Countdown but I love (re)watching 10oo8CDC. Those rare moments when I see the solution before the clock starts are especially precious. I live in Poland and we used to have quite a few really interesting ones (some licensed, some originals). Right now we have only two worth watching left – our 10-person version of 15 to one and a less funny variety of a panel quiz show comparable to "big fat quiz". I yearn for some proper TV.

  17. British game shows are so fun compared to American game shows. 8 out of 10 Cats Does Countdown is one of my favorites. I also love QI, which I think calling it a game show at all is probably just silly.

  18. 4:03 – Does the jumble on-screen at 4:03 have the answer "SPIGOTEER"? Is that another word for "bartender", one who operates the spigots? ("yourdictionary" claims there is no 9-letter anagram for "TPSGEOIER".)

  19. 4:22 – True. There's an episode of "Have I Got" ("A Bit More") "News For You" in which Hannah Fry couldn't multiply 56 by 9 in her head. It made me wonder if she could multiply 56 by 10 in her head. And if she could do 560 minus 56 in her head. I can.

  20. Ah, thanks. I did not know until today that no large number can appear more than once, and that no small number can appear more than twice.

  21. 6:26 – Had that been Jon Richardson, the solution would have been SOMETHING LIKE (there are variations) "75, plus 8 is 83, plus 6 is 89, plus 2 is 91, plus 9 is 100".

  22. I had heard of the show in the 90s but didn't actually see footage from the show itself until 15 years ago. I love challenging myself to see how well I can do.

  23. Didn't notice your avatar, so when that first caption came up — in a video about game shows — my brain shouted out "Blockbusters!"

  24. The moment you asked which small numbers were the best, my brain went to 9, then I thought for a sec and went to 7. It probably means nothing but it made me laugh that my intuition was spot on for no proper reason xD

  25. Many thanks for this excellent analysis.

  26. Excellent video and explanations. Thanks!

  27. 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!

  28. 532211 allows 5^2*(3-1)*2 = 100 or (5+3+2)^2 = 100 etc… but I didn't know they disallow exponents.

  29. Occasionally Carol or Rachel knows immediately that a number is not possible with the set.
    But I've never found any explanation of how?

  30. yet another mindless little parrot conflating England with the entire union it's part of.

  31. my most watched game show is probably richard osmans house of games

  32. Whoever said you're limited to the five basic operators?

  33. "Erm yes Jimmy I got it!"

    – Totally Aisling Bea

  34. im dogshit at maths but i watched this whole video haha.

  35. Is it possible to calculate quickly 'near misses', thus as a strategy avoiding getting timed out?

  36. 17:18 842 different targets? That's not what "amount reachable" means. It's "upto this number" but doesn't necessarily include all numbers smaller than it, and you only start at 100 anyway. Also, the table is wrong, it should be number reachable.

  37. "We'd also get through two more mathematicians" This made me laugh way more than it really should have done.
    I guess I'm in a small minority that appreciates a joke of this intellectual caliber.

  38. When choosing say 4 small numbers, it's not 10-choose-4 since zero is not an option. It's only 9-choose-4.

  39. If you’re trying to seduce Rachael, you’re saying all the right things. 🤣

  40. I could only see this kind of show taking off in the US if it highlighted god and guns, or taking pride in not countin so good. Sigh. I’m no rocket surgeon, but I despise my country’s so common praising of anti intellectualism. What a waste of a perfectly useable brain.


    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.

Leave a Reply

Your email address will not be published.