# Your Solutions - Stage 3 & 4

##### Stage: 4 Challenge Level:

Four jewellers share their stock. Can you work out the relative values of their gems?

### Counting Factors

##### Stage: 3 Challenge Level:

Is there an efficient way to work out how many factors a large number has?

### An Equilateral Triangular Problem

##### Stage: 3 Challenge Level:

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

### Star Polygons

##### Stage: 3 Challenge Level:

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

### Angles in Three Squares

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

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

### Polygon Pictures

##### Stage: 3 Challenge Level:

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

### Who's the Best?

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

Which countries have the most naturally athletic populations?

### Charting Success

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

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

### Spots and Measles

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

99% of people who have measles have spots. Ben has spots. Do you think he has measles?

### Do Rare Events Happen?

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

I'd be very surprised if I had three children all with the same birthday, but I read in the paper that it happened to one family...

### The ELISA Test

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

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

### Gabriel's Problem

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

### Journey to School

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

How risky is your journey to school?

### Risk and Crime

##### Stage: 4 Challenge Level:

Are you at risk of being a victim of crime? How does your perception of that risk compare with the facts and figures?

### Trusting the Tabloids

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

Can you match the cards and figure out whether the tabloid headlines can be trusted?

### Puzzling Place Value

##### Stage: 4 Challenge Level:

Can you explain what is going on in these puzzling number tricks?

### Reversals

##### Stage: 3 Challenge Level:

Where should you start, if you want to finish back where you started?

### Making a Difference

##### Stage: 3 Challenge Level:

How many different differences can you make?

### Matching Criminals

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

DNA profiling is an invaluable tool for the police. However, when it comes to probability, things aren't always as straightforward as they seem.