## Tuesday, 8 July 2008

### The 118118 Challenge

118118 is a directory enquiries phone number in the UK that has recently expanded to "answer any question you put to us, no matter how big or small."

So we thought we might test them out with some of the unsolved questions from our show, and then some maths.

Listen here, with the voice of 118118 played by the AT&T Text-to-Speech synthesiser.

Marc: Can you recycle condoms?
118118: In general, condoms are made of latex and are not recyclable. It is probably better to dispose of your used condoms in the rubbish. Thank you!
Verdict: Pretty much what we came up with too. To read more about recycling condoms, see the Mr Science article Recycling Condoms.

Marc: How many colours to do you need to colour a political map of the world such that no two bordering countries are the same colour?
118118: Four colour theorem: any plan separated into regions, the regions may be coloured using 4 colours in such a way that no 2 adjacent regions receive the same.
Verdict: Pretty good. The four colour theorem is correct, although it is just a theorem and so no one has conclusively proven that you only need 4 colours to colour the map. See the Plus article The origins of proof IV: The philosophy of proof.

Marc: Is there a formula for solving quintic equations, like there is for quadratic equations?
118118: There is no formula for general quintic equations over the rationals in terms of radicals. Some can be solved by factorising into radicals. Thank you!
Verdict: Correct. For more on the quintic, see the Plus article The equation that couldn't be solved.

Marc: Is the Mandelbrot set locally connected?
118118: The Mandelbrot set is a set of points in the complex plane. It is a compact set, contained in the closed disk of radius 2 around the origin. Thanks!
Verdict: Well, that's correct but not an answer. That the Mandelbrot set is locally connected is an outstanding conjecture. To read more about the Mandelbrot set, see the Plus article Unveiling the Mandelbrot set.

Then I got my Plus co-editor Marianne involved, and she was less forgiving...

Marianne: Can any even number bigger than two be written as the sum of two primes?
118118: Every even number bigger than 2 can be written as a sum of two
primes. Thank you.
Marianne: But that's wrong!
118118: 2 is the only even prime.
Marianne: But that's got nothing to do with the question.
118118: Every even number bigger than 2 can be written as a sum of two primes.
Marianne: Still wrong.
118118: No charge. Please direct any questions to our customer service
department.
Verdict: It was a bit harsh asking 118118 an unproven conjecture. The Goldbach conjecture postulates that all even number greater than 4 can be written as the sum of two odd primes. To read more about the Goldbach conjecture, see the Plus article Mathematical mysteries: the Goldbach conjecture.

Finally, a couple of big questions.

Marc
: Can science disprove God?
118118: It's a personal decision for you to make. Everything was "created", therefore decide if you believe it was by someone, some being or a metaphysical force.

And an even bigger one...

Should you have sex the night before a big sporting event? (see map)

 Yes - Good for your performance: (32%) No - Bad for your performance: (25%) I'll take it when I can get it: (24%) Only if you're married: (5%) Makes absolutely no difference to your performance: (15%)