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I am replying to the problem “take 3 from 5”. I first thought about how to represent this problem. I knew that numbers fall into three categories, numbers that are 1 more than a multiple of three, numbers that are 2 more than a multiple of three and numbers that are a multiple of 3. I represented the numbers that are one more than a multiple of three as x, numbers that are 2 more than a multiple of 3 as y, and numbers that are a multiple of 3 as z.

x+y+z= a multiple of 3.
Example: 1+2+3=6

z+z+z=a multiple of 3
example: 3+3+3=9

y+y+y=a multiple of 3
Example: 2+2+2=6

x+x+x=a multiple of 3
Example: 1+1+1=3

Since every number has to be either x, y or z, and that these combinations work,
It is impossible to produce a set of 5 whole numbers that any 3 of them do not add up to a multiple of 3.
This is because in a group of 5, it is not possible to have no groups of 3, whilst also not having one of each type.