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problem

Favourite

Gutter

14 to 16

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

problem

Sometimes we lose things

7 to 11

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

problem

Rachel's problem

14 to 16

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

problem

Cocked hat

16 to 18

Sketch the graphs for this implicitly defined family of functions.

problem

Long short

14 to 16

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

problem

Folding fractions

14 to 16

What fractions can you divide the diagonal of a square into by simple folding?

problem

Two on five

5 to 11

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?