# June 2003, All Stages

## Problems

### Tricky Track

##### Stage: 2 Challenge Level:

In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?

### Graphing Number Patterns

##### Stage: 2 Challenge Level:

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

### The Pet Graph

##### Stage: 2 Challenge Level:

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

### Hoops/rope

##### Stage: 2 Challenge Level:

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

### Sealed Solution

##### Stage: 2 Challenge Level:

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

### Same or Different?

##### Stage: 2 Challenge Level:

Anna and Becky put one purple cube and two yellow cubes into a bag to play a game. Is the game fair? Explain your answer.

### Sets of Numbers

##### Stage: 2 Challenge Level:

How many different sets of numbers with at least four members can you find in the numbers in this box?

### Racing Odds

##### Stage: 3 Challenge Level:

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

### Only Connect

##### Stage: 3 Challenge Level:

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

##### Stage: 3 Challenge Level:

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

### Tree Tops

##### Stage: 3 Challenge Level:

A manager of a forestry company has to decide which trees to plant. What strategy for planting and felling would you recommend to the manager in order to maximise the profit?

### In a Box

##### Stage: 3 Challenge Level:

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

### 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.