Take Three from Five
Take Three from Five printable sheet
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.
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.
Click here for a poster of this problem.
Although number theory - the study of the natural numbers - does not typically feature in school curricula it plays a leading role in university at first year and beyond. Having a good grasp of the fundamentals of number theory is useful across all disciplines of mathematics. Moreover, problems in number theory are a great leisure past time as many require only minimal knowledge of mathematical 'content'.
We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of this resource.
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