Countdown Game Show - Number Rounds (21 September 2023) 

Also, the final game was a 4L trick special a sort of play on numbers with James Martins method for 952. 75-6=69 69*6*50=20700 20700+100=20800 20800/25=832

I saw that 961 immediately. Surprised Rachel didn’t…shocked actually. Same as the first answer.

Rach can't be uber nerds like us...

There is someone with a solver backstage who probably fed her the answer the first time. She's definitely good, don't get me wrong, but she appears even better than what she is thanks to backstage assistance.

@@syntaxlost9239 my inlaws have been to a recording of this show...she's a math whiz with a pen and paper. No 1 is feeding her the answer...sometimes she can't come up with the answer or there is no answer that's why you can only sometimes be 1 or 2 away...

@@boybawang1981 So, you're correct, she is very good at mental arithmetic. Nobody will ever dispute that. She relies heavily on divisibility checks which is a common strategy amongst top apterites as it's fast and has a high hit rate. However, there are a number of solves that come up which really can't be found without a graph search. So possible, but not consistently possible for humans in a reasonable time period. Those sorts of answers are typically fed to her off camera. It's nothing nefarious, it just makes filming more efficient. Your in-laws simply attended a filming when it wasn't needed or they didn't catch it.

@@syntaxlost9239 Well...my inlaws live near the studio where this is filmed (Manchester), they been to many tapings. They film 5 or more episodes a day so they have plenty for airing and sometimes Rachel CAN'T get the answer and it will be like she stated (Her Homework). For the most part, they say she gets to the answer, but sometimes, it takes more than the allotted 30 seconds. The #'s Rounds tend to be harder on Countdown than on 8 Out Of 10 Cats Does Countdown, so it might take her a little longer to get to the solution.

I remember the famous 952 solution quite well. Carol Vorderman was very surprised he even got it, by going up into the numbers he did. Having looked on the Countdown Solver on Maths Resources (I don't have the mathematical ability to even try and work out these tricky ones!) it appears that going up to 20800 and dividing by 25 is the only solution, so the one-away that the contestant got was a good solution that they should be proud of.

@@TheSpotify95 There is another possible solution in that game, but it's a fairly tricky thing to spot as well. It requires using the large numbers to create ratios, in this case 75 / 59 as 3 : 2. The numbers were 100, 75, 50, 25, 6, 3 --> 952 So the other viable solution is to do this: 100 + 3 = 103 75 x 6 = 450 450 / 50 = 9 103 x 9 = 927 927 + 25 = 952 The thing about James Martin's solution is that you don't have to know what the huge numbers sum to in order to do the problem. All you have to do is keep in mind the smaller numbers that the large ones represent once you've divided by whatever it's going to be. The templates for the solutions are as follows: (75 x 50 -/+ 100) / 25 = 146 / 154 (100 x 50 -/+ 75) / 25 = 197 / 203 (100 x 75 -/+ 50) / 25 = 298 / 302 And since the commutative property holds for multiplication, you can either choose to add something to, for example, the 100 or to the 50 and then multiply by 2 (50 / 25) or 4 (100 / 25) before adding or subtracting 3 (75 / 25). For example, this is the _only_ way of solving for 235 with the starting numbers 100, 75. 50, 25, 4, and 2. 4 x 2 = 8 50 + 8 = 58 100 x 58 = 5800 5800 + 75 = 5875 5875 / 25 = 235 I've added the 8 to the 50, so the 100 stands for 4 and the 75 for 3, thus the simplified equation is (50 + 4 x 2) x 4 + 3 = 235. And if you use one of the small numbers to multiply by, you can sometimes reach targets even into the 900s (or beyond, but that doesn't matter for _Countdown_ ). And another way you can reach targets in the region of the 900s is through the 937.5 rule, because 75 x 50 x 25 / 100 = 937.5. Again, the commutative property means you can either do [75 x 50] x 25 / 100, essentially dividing by 4, or [75 x 25] x 50 / 100, essentially dividing by 2. You can even do [50 x 25] x 75 / 100, but that's less useful because the interim number has to be a multiple of 4 and the targets must be a multiple of 3. That's because of the mathematical relationship of the 75 to the 100 and the fact that you're not allowed decimals or fractions. Still, it helps in some cases. And by adding or subtracting one of the small numbers, you can get targets far away from 937.5. For example, another solve on a par with James Martin's 952 was Jon O'Neill's 813 calculation. He was given the numbers 100, 75, 50, 25, 10, 1, and he did it thus: 75 - 10 = 65 65 x 25 = 1625 1625 + 1 = 1626 1626 x 50 = 81300 81300 / 100 = 813 The last two steps were just a bit of fun, but the really impressive fact is that he saw that because he was going to be dividing by 2, essentially, in the end, that starting with 75 - 10 would be equivalent of subtracting 250 from the interim sum (75 x 25 is 1875, so it was 1625) and 125 from 937.5, thus giving him 812.5. Then all he needed to do was find a way to round up that 0.5 to a whole number, but the other number was a 1, which is 0.5 when divided by 2.

Nice! And if you'd had the 7 and 6 switch places, you would've gotten 31x31=961... :)

Presumably she doesn't get it sometimes, or they would show it.

Yeah that's the only way you can get to 832. This is the same approach James martin used on his famous 952 calculation. And yes, the "something" is a 5 digit number. I would be very pleased with getting a one-away on this one.

It annoys me that people think they have to beat the clock and not use a calculator........ PAUSE IT ... pen pad calc at the ready!!! Do you think daredevils start with the toughest stunt and no net or even a crash helmet? I keep going back over these and either I'm remember how I did it 3-6-9 weeks ago or I'm getting better at mental arithmetic in general, but even the new eps don't require me to reach for the calculator as much. Like the old joke says: practice man... practice.

First one I found easy enough with (8*3)+7 for 31, 25+6 for 31 and then simply multiplying them.

On the contrary, I did it at once. I'm used to seeing stuff like this because I play _Countdown_ numbers games for fun and four-large is my favorite selection. For example, here's a recent one along the same lines that the computer threw at me: 100, 75, 50, 25, 7, 6 --> 970 The _only_ way it can be done under the _Countdown_ rules is as follows: 75 - 6 = 69 69 x 50 = 3450 3450 x 7 = 24150 24150 + 100 = 24250 24250 / 25 = 970 It's just a matter of using the large numbers to stand in for smaller ones. In this case, 50 / 25 = 2 and 100 / 25 = 4. So the simplified form of the equation that I did in my head was (75 - 6) x 2 x 7 + 4 = 970.

U cheated!? So ur a phony!? A Big Fat Phony!!

If you're used to how Countdown works, especially with manipulating the large numbers, and you have the math arithmetic to do so, then it can definitely be done. Though given Rachel couldn't get there within the 30 seconds, it's a tough cookie. It's the same approach used on the famous 952 example. But if you don't know that approach with the large numbers, you'd be very pleased in getting a one-away, which there were plenty of solutions for.

They do talk about using that method strategically also 6 small can flummox most people.

@user-wm3bf7pi3u My heart sinks with those as well. It just seems a bit unsporting to me.

I would think it’s the other way around. 4L is something you can learn loads of tricks for so really someone could choose 4L to win the numbers round over your opponent. Also 4L has the potential to make for really beautiful solutions that go into the tens of thousands halfway. If I were on countdown I would do 4L every time