Take Three from Five

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You might like to start by looking at What Numbers Can We Make?
  
Choose any five positive whole numbers.
Can you select three that will add up to a multiple of 3?
 

 
For example:
If you start with 1, 5, 10, 13 and 18,
you can select 1, 10 and 13 which add up to 24.

 
 
 
  
 
 
Choose another five positive whole numbers.
Can you select three again that will add up to a multiple of 3? 
 
 
 
 
Is it always possible to find three numbers that will add up to a multiple of 3 from any set of five positive whole numbers?

Can you explain why?


You can input five numbers in the interactivity below and the computer will try to select three that add up to a multiple of 3. Will it always be able to find three that add up to a multiple of 3?
 
A poster of this problem is available here.

Full Screen Version

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Published October 2003.