Overturning Fracsum

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

Rudolff's Problem

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

What's it Worth?

Stage: 3 and 4 Challenge Level:

If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...

Each symbol has a numerical value. The total for the symbols is written at the end of each row and column.

Can you find the missing total that should go where the question mark has been put?

Grid containing symbols.

Once you've had a go at the problem, click below to see how Charlie, Alison and their friends began working on the task.

Can you take each of their starting points and develop them into a solution?

Method 1

Method 2

Method 3

Method 4

Method 5

Method 6

Method 7

Method 8

Can you find any other methods to solve the problem?

You can apply these methods to other versions of the problem. This spreadsheet can be used to generate lots of different examples.

Here are three other problems that can be solved using similar strategies:

Sweet Shop

Letterland

Children at Large