# May 2003, Stage 4&5

## Problems

### Excel Technique: LCM & HCF (or GCD)

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

Learn how to use the Excel functions LCM and GCD.

### Excel Interactive Resource: Fraction Addition & Fraction Subtraction

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

Use Excel to practise adding and subtracting fractions.

### Excel Investigation: Fraction Combinations

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

Choose four numbers and make two fractions. Use an Excel spreadsheet to investigate their properties. Can you generalise?

### Knight Defeated

##### Stage: 4 Challenge Level:

The knight's move on a chess board is 2 steps in one direction and one step in the other direction. Prove that a knight cannot visit every square on the board once and only (a tour) on a 2 by n board. . . .

### Magic W

##### Stage: 4 Challenge Level:

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### LOGO Challenge - Following On

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

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

### Witch of Agnesi

##### Stage: 5 Challenge Level:

Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.

### Teams

##### Stage: 5 Challenge Level:

Two brothers belong to a club with 10 members. Four are selected for a match. Find the probability that both brothers are selected.