problem
Shopping basket
Age
11 to 16
Challenge level
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
problem
Parabolic patterns
Age
14 to 18
Challenge level
The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.
problem
Vector walk
Age
14 to 18
Challenge level
Starting with two basic vector steps, which destinations can you reach on a vector walk?
problem
Expenses
Age
14 to 16
Challenge level
What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?
problem
Squirty
Age
14 to 16
Challenge level
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
problem
Difference Sudoku
Age
14 to 16
Challenge level
Use the differences to find the solution to this Sudoku.
problem
Funnel
Age
14 to 16
Challenge level
A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?