All entries for November 2009

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?)

Warwick Challenges are mini academic challenges from University of Warwick professors, set via the micro-blogging service Twitter (and also via this blog).
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November 2009

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