*Mathschallenge*

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## December 07, 2009

### Ships That Pass . . .

In the days when people crossed the Atlantic in passenger liners, a ship left London every day at 4.00 p.m. bound for New York, arriving exactly 7 days later.

Every day at the same instant (11.00 a.m. because of the time difference) a ship left New York bound for London, arriving exactly 7 days later.

All ships followed the same route, deviating slightly to avoid collisions when they met.

How many ships from London does each ship sailing from New York encounter during its transatlantic voyage, *not* counting any that arrive at the dock just as they leave, or leave the dock just as they arrive?

## November 23, 2009

### The Curious Incident of the Dog

In Sir Arthur Conan Doyle’s Sherlock Holmes story ‘Silver Blaze’, we find:

‘Is there any other point to which you would wish to draw my attention?’

‘To the curious incident of the dog in the night-time.’

‘The dog did nothing in the night-time.’

‘That was the curious incident,’ remarked Sherlock Holmes.

Here is a sequence: 1, 2, 4, 7, 8, 11, 14, 16, 17, 19, 22, 26, 28, 29, 41, 44

Having taken Holmes’s point on board: what is the next number in the sequence?

## November 16, 2009

### Nice Littler Earner

Smith and Jones were hired at the same time by Stainsbury’s Superdupermarket, with a starting salary of £10,000 per year. Every six months, Smith’s pay rose by £500 compared with that for the previous 6-month period. Every year, Jones’s pay rose by £1,600 compared with that for the previous 12-month period.

Three years later, who had earned more?

## November 09, 2009

### Target Practice

Robin Hood and Friar Tuck were engaging in some target practice. The target was a series of concentric rings, lying between successive circles with radii 1, 2, 3, 4, 5. (The innermost circle counts as a ring.)

Friar Tuck and Robin both fired a number of arrows.

“Yours are all closer to the centre than mine,” said Tuck ruefully.

“That’s why I’m the leader of this outlaw band,” Robin pointed out.

“But let’s look on the bright side,” Tuck replied. “The Total area of the rings that I hit is the same as the total area of the rings you hit. So that makes us equally accurate, right?”

Naturally, Robin pointed out the fallacy...but:

Which rings did the two archers hit? (A ring may be hit more than once, but it only counts once towards the area.)

For a bonus point: what is the smallest number of rings for which this question as two or more different answers?

For a further bonus point: if each archer’s rings are adjacent – no gaps where a ring that has not been hit lies between two that have – what is the smallest number of rings for which this question has two or more different answers?

## November 02, 2009

### Whodunni's Dice

Grumpelina, the Great Whodunni’s beautiful assistant, placed a blindfold over the eyes of the famous stage magician. A member of the audience then rolled three dice.

"Multiply the number on the first dice by 2 and add 5,” said Whodunni. “Then multiply the result by 5 and add the number on the second dice. Finally, multiply the result by 10 and add the number on the third dice.”

As he spoke, Grumpelina chalked up the sums on a blackboard which was turned to face the audience so that Whodunni could not have seen it, even if the blindfold had been transparent.

“What do you get?” Whodunni asked.

“Seven hundred and sixty-three,” said Grumpelina.

Whodunni made strange passes in the air. “Then the dice were...”

What? (And how did he do it?)

## October 26, 2009

### Swallowing Elephants

Elephants always wear pink trousers.

Every creature that eats honey can play the bagpipes.

Anything that is easy to swallow eats honey.

No creature that wears pink trousers can play the bagpipes.

Therefore: Elephants are easy to swallow.

Is the deduction correct or not?

## October 19, 2009

### Digital Cubes

The number 153 is equal to the sum of the cubes of its digits:

1^{3} + 5^{3} + 3^{3} = 1 + 125 + 27 = 153

There are three other 3-digit numbers with the same property, excluding numbers like 001 with a leading zero.

Can you find them?

## October 12, 2009

### The Statue of Pallas Athene

According to a puzzle book published in the Middle Ages, the statue of the goddess Pallas Athene was inscribed with the following information:

“I, Pallas, am made from the purest gold, donated by five generous poets. Kariseus gave half; Thespian an eighth. Solon gave one-tenth; Themison gave one-twentieth. And the remaining nine talents’ worth of gold was provided by the good Aristodokos.”

How much did the statue cost in total? [A talent is a unit of weight, roughly one kilogram.]

## October 05, 2009

### Return of the Maths Challenge!

After a long summer break, the Maths Challenges will be returning to your twitter feed next week!

The Warwick Maths Challenges are based on the books of Professor Ian Stewart.

Prof Stewart’s latest book – Hoard of Mathematical Treasures – is out now and we will bring you some of the best challenges and brain teasers every Monday morning.

## June 22, 2009

### Maths Challenge #10 – Perfect Square

What is the largest perfect square number that uses each digit 123456789 exactly once?