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. Anyone who plays countdown knows their 75 times table…. I am struggling with 8…

  2. Rachel Reilly is impressive but sadly she's very anti-Corbyn. This means she's either right-wing and anti-human-rights, or she's not wise enough to see that she's being manipulated by the right-wing

  3. Huh, in Australia we call the show 'Letters and Numbers' since Countdown was a music show here. We always gave it shit in the idea that "duhh there's letters and numbers on the show" but it was probably a throwback to the french name then.

  4. you might also want to choose a difficult number game (four large for example) if you are ahead after the letters game, and feel that you maybe are generally stronger in the letters game than the numbers game and that your opponent is stronger in the numbers than the letters. What you are doing is counting on your opponent not being able to get the target in a difficult game (even if they get closer than you), and beating them in the letters game only (if you find a 7 letters or better word in the letters game (and beating your opponent in doing so), then you either equal or better your opponent's effort in the numbers game even if they get closer to the target than you (assuming they dont get exactly on the target of course, which is why you want to choose as difficult a game as possible)).

  5. But wait! aren't forced to choose at least 2 large number?

  6. I used to watch Countdown with my Nan if I swung by there after school. I am not really into maths but always enjoyed writing… and yet I was hopeless at the letters rounds and godlike at the maths round.


  7. Honestly the best panel show I feel is QI

  8. Math….Maths is not the plural of math…Math is

  9. Did anyone else notice that to make 64 at 22:00, he used the 4 he had set aside…

  10. Remain indoors. It's wonderful how the brits predicted THE EVENT years before THE EVENT…

  11. 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.

  12. It is not the oldest game show by a long chalk. Generation Game? Call My Bluff? The Golden Shot (1967)? Round Britain Quiz (1947)? What's My Line (1951)? and Spelling Bee (1938)? perhaps you forgot to say "and longest running"?

  13. Do these biases "against" 5 and 10 prevail if we change to a non base-10 number system?
    Would an equivalent emerge?
    Does anyone else find this an interesting question?

  14. Countdown started 41 years ago and this video is 41 minutes long. Coincidence?

    Written at 3:35.

  15. Personally the fact that 25, 50, 75, 100 feel useful but are mathematically less good reminds me of the metric vs imperial divide. Intuitive not equalling raw math power.

  16. In conclusion….. Choose 2 large numbers and 4 small numbers.

  17. why 7 or 9 because star trek ….. had to throw in this childish joke

  18. 21:58 — Some slick editing — the 6×4 inside the parentheses magically corrects itself to 6×5 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.

  19. game show (noun) a TV quiz or other game, usually with prizes, and sometimes with celebrities as competitors. Chambers Dictionary

  20. Still trying to figure out what G28 I34 F30 means

  21. This is a French game show called "Des chiffres et des lettres" (broadcasted since 1972).

  22. i don't understand the fuss about counting the possible number of ways to draw small numbers. There are twenty small numbers. 1-10 and each of their duplicates. What's the problem with the 20-choose-4 approach?

  23. 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.

  24. Countdown has never been the same without Richard.

  25. You can compute 13243 as the coefficient of x^6 in (1+x)^4(1+x+x^2)^10.

  26. another possible option is allowing the large numbers to also contain a 2nd set of duplicates as potential options for inclusion in a game set and how that affects things

  27. In Australia and this is called Letters and Numbers – love Allison and crew

  28. Take the 5,
    times it by 100,
    Then add 8 and 2
    And you get 582

  29. It is not really Britshit tv game, but French created by Armand Jammot as "Des chiffres et des lettres". The very first eposode is aired at France 3 on 19 September 1965.

  30. I appreciate the effort this video took, and loved it. Thanks!!

  31. 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.

  32. Numerical fidelity is an excellent term and I guarantee that the concept is worth looking in to with other algorithms that have a goal and a manipulatable set

  33. Much easier to get to 451 without prime factorization by simply using 25*(9+4+5) – (7-6)

  34. this is like when standupmaths did a python coding solver and viewers wrote C++ solvers that run the full solution in 5s 🤣

  35. 21:59 you wrote 25 + 9 + (6 x 4) when it should have been 25 + 9 + (6 x 5)

  36. Always thought the number was generated by choosing a set of random operations on the selected numbers, therefore always having a simulation.

    Then again, i only know the show from clips on YouTube when 8 out of 10 cats does it 🙂

  37. As for the letters, accented letters are considered to be the same as non-accented ones, which means that an "A" can also be used as an "À" or "Â", a "C" can be used as a "Ç", an "E" can also be used as a "É" or "È" or "Ê" or "Ë", an "I" can be used as an "Î" or "Ï", an "O" can also be used as an "Ô" a "U" can be used as a "Ù" or "Û" or "Ü", and a "Y" can be used as a "Ÿ", and likewise, ligatures are considered to be the same as non-ligatures, which means that an "A" followed by an "E" can also be used as a "Æ", and likewise, an "O" followed by an "E" can also be used as a "Œ", and it's probably for the better, because otherwise, we'd be dealing with essentially over 40 different letters, 42 to be exact.

  38. Liked and subscribed for the understated humour

  39. At 9:01, how can 4 large have 55 combinations? It is basically just all combinations of two numbers. I get that to 45, am I doing something wrong?
    1: 1, 1

    2: 1, 2

    3: 1, 3

    4: 1, 4

    5: 1, 5

    6: 1, 6

    7: 1, 7

    8: 1, 8

    9: 1, 9

    10: 2, 2

    11: 2, 3

    12: 2, 4

    13: 2, 5

    14: 2, 6

    15: 2, 7

    16: 2, 8

    17: 2, 9

    18: 3, 3

    19: 3, 4

    20: 3, 5

    21: 3, 6

    22: 3, 7

    23: 3, 8

    24: 3, 9

    25: 4, 4

    26: 4, 5

    27: 4, 6

    28: 4, 7

    29: 4, 8

    30: 4, 9

    31: 5, 5

    32: 5, 6

    33: 5, 7

    34: 5, 8

    35: 5, 9

    36: 6, 6

    37: 6, 7

    38: 6, 8

    39: 6, 9

    40: 7, 7

    41: 7, 8

    42: 7, 9

    43: 8, 8

    44: 8, 9

    45: 9, 9

  40. Trying to be the nerdiest nerd lands you in the nut-house

  41. 22:36 I wonder how this analysis would change if you restrict your python script to solutions that are humanly possible? For example, if you exclude solutions that are based on prime factors of numbers near the target. Or to be even more restrictive, you could only allow the pitch and put tactic. Would it still be the case that 7 and 9 are the best? I'd guess not.

  42. This seems to assume that humans work like computers, as in the ease of calculation is the same regardless of the numbers involved, which is fundamentally untrue. The human nature of the calculations plays a massive part in the show and this is neglected here. It is probably more interesting to consider easy ways for the human brain to reach various numbers than whether it is possible

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