Choose any three by three square of dates on a calendar page...
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
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.