LAST WORD

WHEN THE ROBOTS TAKE OVER

THE COUNTDOWN CONUNDRUM

Before we finish, let’s briefly move away from estimation and back to the world of precise arithmetic.

In a classic 1997 episode of Channel 4’s word and numbers game Countdown, the host, Carol Vorderman, picked the following six numbers from the table in front of her (four from the top, and two from the third row):

The random number generator then produced a target of 952. The challenge, as always, was for the contestants to use some or all of the numbers on the cards no more than once, to get as close as possible to the target answer of 952.

Perhaps you’d like to have a go now, to see how close you can get.

To get close to the target answer, it’s a huge help to be able to play with numbers. And curiously, even though the task involves ‘exact’ calculation, rough estimates can be handy as a starting point: ‘952 … that’s going to be 9 × 100 and a bit … or 1,000 minus 50ish’.

If you managed to get 950 (two away from the target), give yourself a bronze medal. This is the way that most people get there:

100 × (3 + 6) + 50 = 950.

If you managed to get to within one (953), give yourself a silver medal. To create the 3, you need to spot that:

75 ÷ 25 = 3

950 + 3 = 953.

That would normally be enough to win you the round, but on the programme in question, you would have lost out to the other contestant, James Martin, a PhD maths student who managed to get the exact answer of 952.

Here’s a slightly shortened version of his exchange with Carol Vorderman as he explained how he’d got his answer:

JM:  100 + 6 = 106. Multiplied by 3 …

CV:   … is 318.

JM:  I’d like to multiply it by 75 …

CV:  Multiply 318 by 75? [Laughter] Good grief, I’m going to need my calculator for this one. [Eventually she does the calculation to get 23,850.]

JM:  Now take away 50.

CV:  [More laughter] 23,800.

JM:  And divide it by 25.

CV:  And divide THIS by 25? … [Can barely control hysterics as she writes out the division] Do you know – I think you’re right. That’s incredible!

There are many calculation savants who could do all of the calculations above – and harder ones – in their heads. But James Martin was not a savant, he was just smart at manipulating numbers.

Martin spotted that 106 × 9 = 954, which is 2 away from the target.

There wasn’t a 9 available, but he could get to the same answer by multiplying by 3 twice: first by the 3 on the card, then by 75 ÷ 25, which is also 3. But where would he get the 2 that he needed to subtract from 954? What James spotted was that 50 ÷ 25 = 2, so he could use the 25 twice, by dividing it into 75 and 50.

Written out in full, his solution was this:

This might make it appear that he multiplied 318 × 75 (as you’d do on a calculator), but before multiplying, he divided 75 by 25 first to get 3 and 50 by 25 to get 2. This turned the calculation into:

(106 × 9) – 2.

Which is clever. But it is not genius.

Back in 1997, when that solution was recorded, it’s unlikely that even somebody armed with a computer could have beaten James Martin to the score. But today, there are apps that can solve these Countdown problems instantly. It won’t be too long before a contestant could be wearing a pair of glasses that detects the numbers on the board and displays the solution on the lenses before the timer has even begun to count down.

Which leads to an interesting Countdown conundrum.

We are not far away from a world where we will all be equipped with Artificial Intelligence devices that can solve any numerical puzzles of this kind in an instant. When technology like this becomes readily available, not only will we not need calculators – some might question why we will need to learn any maths at all. When robots can work everything out, will games like Countdown continue to exist?

There will of course be people who scoff at anybody who ‘wastes their time’ figuring out number puzzles when the solution is readily available to them. Just as there are many who scoff at the need to know how to do short division calculations manually, when it can be done by a calculator.

But my prediction is that in 50 years’ time – even when computers can solve just about any numerical problem posed to them almost instantly – people will still have a huge interest in playing number games in their heads. And it won’t just be for a bit of TV amusement. We need to continue to be able to do back-of-envelope calculations without the aid of a calculator, or other artificial device.

Why?

Because we will always need to be equipped to challenge the information that is presented to us, whether it has come from a person or from a computer. If we leave every calculation and every decision to computers, we are in danger of becoming slaves to technology.

And aside from all the practical benefits of being able to do maths on the back of an envelope, there is arguably another that is just as important: doing your own calculations keeps the brain stimulated, and gives it a valuable work-out. Some of us go further, and regard it as fun.