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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.
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:
TOTAL | ||||||
3 | 6 | 5 | 7 | 2 | 18 | |
7 | 17 | 15 | 8 | 10 | 39 | |
20 | 15 | 6 | 11 | 12 | 33 | |
23 | 16 | 9 | 21 | 36 | 48 | |
99 | 57 | 5 | 72 | 23 | 228 | |
312 | 97 | 445 | 452 | 29 | 861 | |
-1 | -1 | 0 | 1 | 1 | 0 |
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.
Click here for a poster of this problem.
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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