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. I've worked on 3 of the gameshows you mentioned in this video! Have you ever considered applying for any yourself?

  2. I am 10000% positive Jon Richardson has watched this video more than once.

  3. I loves maths so much but unfortunately I suck at it so much 🥲

  4. Loved the video. My comment is a bit mal apropos, but you mensioned Pointless. I love the consept. I really do. As a pub quizmaster I even made a catory inspired by Pointless once. I just can't stand the program itself. There is SO MUCH dead time in the form of repetition of rules and small talk with the contestants. Haven't watched it for years though. But as I said: brilliant concept.

  5. I watched the whole video my head hurts …oh how it hurts

  6. I've got the dumbest maths head in the world. I have always been amazed how they can do the pitch bit by altering the big number first. You have explained it so well. Had absolutely no idea that that was how that worked. 🤯🤯🤯🤯

  7. at the end of the video the number 325 glitches and says g28, i34, f30. what that all about?

  8. Just remember, easier is NOT equal to better. You are playing your OPPONENT not the board. If you are better at sums than him, it is better to make the sum harder (but not impossible). If your opponent is better, or you are in a position where both players scoring poorly would be beneficial (IE you are a good amount of points ahead) the best thing to do is to try and make the sum impossible or incredibly easy by going either max large numbers or no large numbers.

  9. I think you'll find there are far older British TV gameshows – such as University Challenge.

  10. One thing I find bizarre, people seem to assume what they get on the screen is what it appears to be. TV is about entertainment. Go watch a filming of a game show and you find out it's really not a game at all.

  11. At the start of the video this game looked far harder because i expected you had to use all your numbers

  12. Are all target numbers achievable? I didn’t think they were.

  13. 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

  14. French exports :
    Wine and boring game shows 😂

    (Je suis français)

  15. new to the channel, what does G28, I34, and F30 mean? Each was only on screen for one frame near then end in the target number area (replaced the 325). Were there more that I missed earlier in the video?

  16. Two things of note:
    * Rachel Riley is one of the hottest women on the face of the earth
    * Definitely check out the comedy spin-off, 8 Out Of 10 Cats Does Countdown, which is very funny

  17. Looking forward to when he gets to the actual point of the video 300000000000 minutes in 🥴

  18. At 34:08, do some of the conclusions change if we score large numbers based on the average scorable points possible (instead of just percent correct)? While 90% may be 0 numbers off, 5% may be 2 numbers off which would offer some intermediate points scored

    I wonder if that “partial credit” would actually positively affect certain combinations more than others

  19. 3:17 the 2nd contestant on University Challenge is Vivian-Neal… Young ones fan?

  20. The factors of 5 may mathematically be harder numbers, but much of that is made up for by the ease of fast calculation, especially for the home viewer.
    The number of people that can rapidly multiply 7*25 is vastly greater than those who can quickly multiply 7*28. Sure, it is just 7*25 + 21, or 7*20 + 54, but multiple operations still take more time. When I see 7*25, 175 just pops into my head. I sadly cannot say the same for 7*28=196. The most intuitive way I get there is 7*30 – 7*2.
    I am only casually familiar with Countdown (Thank you IT Crowd), but if they sprung the large number set on them without giving them a chance to memorize the tables it would be especially difficult.

  21. I watch cats does countdown every single night.

  22. Is the best way to stop your brain from bleeding to stuff tissues into your ears? WOW what a video.

  23. It gets harder when you play Street countdown.

  24. For the first one i ended up with:

    100 x 6 = 600
    5 x 2 = 10
    600 – 10 = 590
    590 – 8 = 582

  25. I’m very much into the maths analysis in this video and enjoyed it greatly but am not above admitting that I giggled when you said “pairs of smalls”.

  26. I wonder if the traditional large numbers would have an advantage in modern humans speed play though because we spend so much time in a base 10 system we just have more practice at working in those multiples.

  27. Wait, I thought the game show was called "8 out of 10 cats does Countdown".
    What the hell did I watch hours of on YouTube at 4am?

  28. If i recall correctly there was an episode of 8 out of 10 cats does countdown that had a target that couldn't be done. But i could be wrong. It's been a year since i binged them all

  29. Is countdown math useful anywhere else? The only thing that comes close would be combining resistors to get a specific resistance, but usually close counts in circuits as well.

  30. Interesting that 25-50-75-100 are mathematically the worst to work with, but they are probably easier for our base-10 brain

  31. Countdown is based on a French tv game called "des chiffres et des lettres" created by Armand Jammot in 1965 and still running

  32. At 30:15 I’m not understanding how dividing by 25 at the end is the same as dividing the 75 and 50. Doesn’t the denominator affect every part of the numerator, Including the 106 and 3?

  33. Not sure why people outside the UK wouldn’t know countdown. I work in IT, so I watch The IT Crowd, so I googled countdown after that one episode, and then I watched every countdown clip on the internet. Seems simple enough, yeah?

  34. What about the total you have so far arrived at?

  35. Ok…. I didn't understand that you could leave some numbers out. But it's fun to keep going until you use them all.

  36. The oldest British TV game show … invented by the French.

  37. I watched the very first episode of countdown as it was the very first programme aired on channel 4. (If I remember correctly)

  38. 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.

  39. I legitimately grinned at the flashing "Remain Indoors"… one of my favourite Mitchell & Webb sketches.

  40. you need to remove the 999 limit on calculations, many solutions will be available with a division of a number that is greater than 999.

  41. It has two coinciding running's of Countdown. The traditional Count down which is a legitimate game, then there is "8 out of 10 cats does Countdown" which is the same game, but with a lot of jokes and British Humour involved being still done by Suzie Dent (Dictionary Corner) and Rachel Riley mentioned in this video. But everyone else is a Comedian and they take the piss out of each other and come up with new gags all the time and the wit is perfect.

  42. Enjoyed it, thank you. My mum was on Countdown in the 80's.

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