# February 2003, Stage 4&5

## Problems

### Excel Technique: LOOKUP Functions

##### Stage: 3 and 4 Challenge Level:

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

### Excel Interactive Resource: Equivalent Fraction Bars

##### Stage: 3 and 4 Challenge Level:

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

### Excel Investigation: Happy Numbers

##### Stage: 3 and 4 Challenge Level:

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

### Marbles in a Box

##### Stage: 3 and 4 Challenge Level:

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

### In a Spin

##### Stage: 4 Challenge Level:

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

### Plum Tree

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

Label this plum tree graph to make it totally magic!

### Magic Caterpillars

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

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

### Golden Powers

##### Stage: 5 Challenge Level:

You add 1 to the golden ratio to get its square. How do you find higher powers?

### Folium of Descartes

##### Stage: 5 Challenge Level:

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.