*Mathschallenge*

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## June 15, 2009

### Maths Challenge #9 – Ring a–Ring a–Ringroad

The M25 motorway completely encircles London, and in Britain we drive on the left. So if you travel clockwise around the M25 you stay on the outside carriageway, whereas travelling anti-clockwise keeps you on the inside carriageway, which is shorter. But how much shorter?

The total length of the M25 is 188km (117 miles), so the advantage of being on the inside carriageway outght to be quite a lot – shouldn’t it?

Suppose that two cars travel around the M25, staying in the outside lane – one going clockwise and one going anti-clockwise. Also suppose that the distance between these two lanes is always 10 metres (to make it specific).

How much further does the clockwise van travel than the anti-clockwise one? You should also assume that the roads all lie in a flat plane.

## June 08, 2009

### Maths Challenge #8 – Family Occasion

'It was a wonderful party,' said Lucilla to her friend Harriet.

'Who was there?'

'Well - there was one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law and one daughter-in-law.'

'Wow! Twenty-three people!'

'No, it was less than that. A lot less.'

What is the *smallest *size of party that is consistent with Lucilla's description?

## June 01, 2009

### Maths Challenge #7 – How Deep is the Well?

I drop a rock down a well, and it takes 6s to reach the bottom. If gravity is 10m/s², how deep is the well?

## May 26, 2009

### Maths Challenge #6 – What Day is It?

Yesterday, Dad got confused about which day of the week it was. 'Whenever we go on holiday, I forget,’ he said.

‘Friday,’ said Darren.

‘Saturday,’ his twin sister Delia contradicted.

‘What day is tomorrow, then?’ asked Mum, trying to sort out the dispute without too much stress.

‘Monday,’ said Delia.

‘Tuesday,’ said Darren.

‘Oh, for Heaven’s sake! What day was it yesterday, then?’

‘Wednesday,’ said Darren.

‘Thursday,’ said Delia.

'Grrrrr!’ said Mum, ‘each of you has given one correct answer and two wrong ones.’

What day is it today?

## May 18, 2009

### Maths Challenge #5 – Après–le–Ski

The little-known Alpine village of Après-le-Ski is situated in a deep mountain valley with vertical cliffs on both sides. The cliffs are 600 metres high on one side and 400 metres high on the other. A cable runs from the foot of each cliff to the top of the other cliff, and the cables are perfectly straight.

At what height above the ground do the two cables cross?

(Picture not to scale)

## May 11, 2009

### Maths Challenge #4 – How Old Was Diophantus?

Diophantus’ childhood lasted one sixth of his life. His beard grew after one-twelfth more. He married after one-seventh more. His son was born five years later. The son lived to half his father’s age. Diophantus died four years after his son. **How old was Diophantus when he died?**

###### Who was Diophantus?

"Diophantus was probably Greek and he lived in ancient Alexandria. Some time around AD 250 he wrote a book about solving algebraic equations - with a slight twist: the solutions were required to be fractions, or better still, whole numbers. Such equations are called *Diophantine equations* to this day."

Find out more in *Professor Stewart's Cabinet of Mathematical Curiosities* by Ian Stewart

## May 05, 2009

### Maths Challenge #3 – Scrabble Oddity

Writing about web page http://www2.warwick.ac.uk/newsandevents/audio/more/mathschallenge/?podcastItem=scrable_odity_question_master.mp4

Scrabble Oddity: Which positive integer is equal to its letter score in scrabble?

## April 27, 2009

### Maths Challenge #2 – Pig in a Field

A pig tied to the corner of a 100m-sided equilateral triangle field can cover half its area. How long is the rope?

### Maths Challenge #1 – Digital Century

Place 3 maths symbols between the digits 123456789, in that order, so that the result = 100