This problem builds on What Numbers Can We Make?
Take a look at the video below.
Will Charlie always find three integers that add up to a multiple of 3?
If you can't see the video, click below to read a description.
Charlie invited James and Caroline to give him sets of five integers (whole numbers).
Each time he chose three integers that added together to make a multiple of 3:
Charlie challenged Caroline and James to find a set of five integers that didn't include three that added up to a multiple of 3.
Can you find a set of five integers that doesn't include three integers that add up to a multiple of 3?
If not, can you provide a convincing argument that you can always find three integers that add up to a multiple of 3?
You can test sets of five integers using the interactivity below.
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of this resource.