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##### Stage: 5 Short Challenge Level:

Choose any whole number n, cube it, add 11n, and divide by 6. What do you notice?

##### Stage: 5 Short Challenge Level:

What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?

##### Stage: 5 Short Challenge Level:

Can you solve this inequalities challenge?

##### Stage: 5 Challenge Level:

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

##### Stage: 5 Short Challenge Level:

Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

##### Stage: 5 Challenge Level:

Can you invert this confusing sentence from Lewis Carrol?

##### Stage: 5 Challenge Level:

A weekly challenge concerning prime numbers.

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16
students or enthusiastic younger students.

##### Stage: 4 and 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 5 Short Challenge Level:

An arithmetic progression is shifted and shortened, but its sum remains the same...

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 4 and 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 5 Short Challenge Level:

Can you rotate a curve to make a volume of 1?

##### Stage: 5 Short Challenge Level:

What can you deduce about the gradients of curves linking (0,0), (8,8) and (4,6)?

##### Stage: 5 Short Challenge Level:

Is this surd sum exactly 3?

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16
students or enthusiastic younger students.

##### Stage: 5 Short Challenge Level:

Trigonometry, circles and triangles combine in this short challenge.

##### Stage: 5 Short Challenge Level:

When you stack powers, how do you evaluate them?

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 5 Short Challenge Level:

Find the location of the point of inflection of this cubic.

##### Stage: 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 4 and 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.

##### Stage: 4 and 5 Short Challenge Level:

A weekly challenge: these are shorter problems aimed at Post-16 students or enthusiastic younger students.