Countdown puzzle: Make 952 from 100, 75, 50, 25, 6 and 3

Have a go at this one before you read on. It's pretty straightforward to make 953 (exactly as the poor antagonist, Gerald, in this story does):

100 × (6 + 3) = 900

900 + 50 = 950

75 ÷ 25 = 3

950 + 3 = 953.

Well done, seven points, audience applause. But 952 is a much trickier proposition. Once you've had a look at it, look at this video of James Martin working it out before the clock goes boodoo doodoo diddlydip ping!

There is almost nothing I don't like about this video, from the chuckles when James says 'four from the top', to Carol's incredible jacket to James's sheepish grin at the end. He's not 100% sure he's got it. He stumbles over the explanation. Then there's her total astonishment when he says to multiply by 75 ("multiply *THIS?* By *75?!*") and her unsureness that he's got it right. It's an amazing bit of mental arithmetic under pressure, and I salute him for pulling it off. The only thing I don't like is that they made poor Gerald explain his answer which was, in fairness, a creditable attempt given the difficult numbers.

I tried to solve this puzzle and didn't get close to it. But having seen the answer, I can explain the thought process behind it. But certainly not in 30 seconds!

The basic idea is exactly what you'd expect: start with 9 × 100 and figure out how to get the remaining 52.

An average Countdown player would probably think "I know - 54 is 9 × 6, so 954 is 9 × 106." Again, this is almost exactly what James did, only with an added stroke of genius. To get 954, you can do:

(100 + 6) × 3 × 75 ÷ 25 = 954

That might seem like it's worse than before - you're two away rather than one. However, there's a key difference: you have the 50 left over. Also, 50 ÷ 25 = 2... which means we might be on to something. If you take off the 50 before you divide by 25, you're going to get 952!

((100 + 6) × 3 × 75 - 50) ÷ 25 = 952.

Boom!

One thing that you might not pick up on if you're not looking for it: James doesn't know the answer to 318 × 75. When he did the sum, he simply wasn't interested in the answer to that; he was just applying distributive laws to get to his answer.

In summary, James Martin came to the Countdown studio to drink milk and kick ass. And he'd just finished his milk.

## Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.