What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
This problem builds on What Numbers Can We Make?
Take a look at the video below. Will Charlie always find three numbers that add up to a multiple of 3?
If you can't see the video, click below to read a description.
Charlie challenges Caroline and James to find a set of five whole numbers that doesn't include three that add up to a multiple of 3.
Can you come up with a set of five whole numbers that don't include a subset of three numbers that add up to a multiple of 3?
You can use the interactivity below to input sets of five numbers and test whether there are three numbers that add up to a multiple of 3.
Full Screen Version
If you can't find a set of five whole numbers where it's impossible to choose three that add up to a multiple of three, convince us that no such set exists.
Click here for a poster of this problem.