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Citizen 10th December 2010 - the City of London School

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Friday <strong>December</strong> 10 2009<br />

Puzzle Page<br />

Maths Puzzle<br />

Daniel Hu 5H <strong>Citizen</strong> Maths Puzzler<br />

Question<br />

If both ‘p’ and ‘p cubed plus three’ are<br />

prime, what could p be? Prove that you<br />

have found all possible ps.<br />

Hints:There is only one even prime, and<br />

that is 2.<br />

The cube <strong>of</strong> an even number is even. The<br />

cube <strong>of</strong> an odd number is odd. This means<br />

cubing conserves parity.<br />

Adding 3 to an even number makes it odd.<br />

Adding 3 to an odd number makes it even.<br />

This means that adding 3 changes parity.<br />

Note: Parity is whe<strong>the</strong>r something is even<br />

or odd i.e. whe<strong>the</strong>r it is divisible by 2 or<br />

not. We say that 1 has parity odd.<br />

CITY QUIZ<br />

1.Which two US manned space programmes<br />

preceded Apollo?<br />

2.How many Asian countries start with <strong>the</strong><br />

letter ‘B’?<br />

3.Until 1949, what was Indonesia called?<br />

4.With 39 years and 321 days, who is <strong>the</strong><br />

oldest player to debut in a FIFA World Cup<br />

tournament?<br />

5.Which famous conqueror’s title translated<br />

means ‘ocean ruler’?<br />

6.Its capital is Valletta and <strong>the</strong> largest city<br />

is Birkirkara. Where?<br />

7.Which fabled writer is credited with <strong>the</strong><br />

following words <strong>of</strong> wisdom?: “Don’t<br />

count your chickens before <strong>the</strong>y hatch”<br />

8.Which clove like scented flower, also<br />

a registered trade mark, is known as ‘<strong>the</strong><br />

flower <strong>of</strong> God’?<br />

9.What is <strong>the</strong> more common name for<br />

triatomic oxygen?<br />

10.Twenty five square feet <strong>of</strong> land in which<br />

US state <strong>of</strong>ficially belongs to <strong>the</strong> UK?<br />

Page 11

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