# June 2003, Stage 4&5

## Problems

### Excel Technique: Composite Bar Charts

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

Learn how to use composite bar charts in Excel.

### Excel Interactive Resource: Fraction Multiplication

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

Use Excel to explore multiplication of fractions.

### Excel Investigation: Difference Tuples

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

Use an Excel spreadsheet to investigate differences between four numbers. Which set of start numbers give the longest run before becoming 0 0 0 0?

### Chances Are

##### Stage: 4 Challenge Level:

Which of these games would you play to give yourself the best possible chance of winning a prize?

### Loopy

##### Stage: 4 Challenge Level:

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?

### LOGO Challenge - Recollection

##### Stage: 3, 4 and 5 Challenge Level:

Several procedures to think about but there are several things you can do to help yourself such as breaking the procedures down stepwise (rather than into smaller peices) What does the first line do?. . . .

##### Stage: 5 Challenge Level:

Find all positive integers a and b for which the two equations: x^2-ax+b = 0 and x^2-bx+a = 0 both have positive integer solutions.

### W Mates

##### Stage: 5 Challenge Level:

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

### Mechanical Integration

##### Stage: 5 Challenge Level:

To find the integral of a polynomial, evaluate it at some special points and add multiples of these values.