## Problems

##### Age 11 to 14 Challenge Level:

If it takes four men one day to build a wall, how long does it take
60,000 men to build a similar wall?

##### Age 11 to 14 Challenge Level:

ABC is an equilateral triangle and P is a point in the interior of
the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP
must be less than 10 cm.

##### Age 11 to 14 Challenge Level:

Suppose you are a bellringer. Can you find the changes so that,
starting and ending with a round, all the 24 possible permutations
are rung once each and only once?

##### Age 11 to 14 Challenge Level:

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?

##### Age 11 to 14 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?

##### Age 11 to 14 Challenge Level:

Consider all of the five digit numbers which we can form using only
the digits 2, 4, 6 and 8. If these numbers are arranged in
ascending order, what is the 512th number?

##### Age 11 to 14 Challenge Level:

Anne completes a circuit around a circular track in 40 seconds.
Brenda runs in the opposite direction and meets Anne every 15
seconds. How long does it take Brenda to run around the track?

##### Age 11 to 14 Challenge Level:

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

##### Age 11 to 14 Challenge Level:

Imagine you have six different colours of paint. You paint a cube
using a different colour for each of the six faces. How many
different cubes can be painted using the same set of six colours?

##### Age 14 to 16 Challenge Level:

A 10x10x10 cube is made from 27 2x2 cubes with corridors between
them. Find the shortest route from one corner to the opposite
corner.

##### Age 14 to 16 Challenge Level:

Consider a watch face which has identical hands and identical marks
for the hours. It is opposite to a mirror. When is the time as read
direct and in the mirror exactly the same between 6 and 7?

##### Age 14 to 18 Challenge Level:

Investigate the sequences obtained by starting with any positive 2
digit number (10a+b) and repeatedly using the rule 10a+b maps to
10b-a to get the next number in the sequence.

##### Age 16 to 18 Challenge Level:

Solve an equation involving the Golden Ratio phi where the unknown
occurs as a power of phi.

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