Your Solutions - Stage 3 & 4

An Equilateral Triangular Problem

Stage: 3 Challenge Level: Challenge Level:1

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

Star Polygons

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:1

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: Challenge Level:1

Which countries have the most naturally athletic populations?

Charting Success

Stage: 3 and 4 Challenge Level: Challenge Level:1

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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: Challenge Level:1

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: Challenge Level:1

How risky is your journey to school?

Risk and Crime

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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: Challenge Level:2 Challenge Level:2

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

Puzzling Place Value

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Reversals

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Making a Difference

Stage: 3 Challenge Level: Challenge Level:1

How many different differences can you make?

Matching Criminals

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

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