Here's a fun math thing:
Imagine building a set of non-negative integers, starting with zero. As you check increasing numbers, you add it to the set if doing so does NOT create a subset of three items in your set that form an equally-spaced series. For example:
0,1,2 is not okay, since 2-1 = 1 and 1-0=1.
0,1,3 is okay since 3-1=2 and 1-0=1.
0,1,3,4 is okay.
0,1,3,4,5 is NOT okay, since 1-3-5 is a 2-step series, and 3,4,5 is a 1-step series (2 fouls).
And so on.
Numbers in between elements in this test don't interfere with it. Imagine the flawed set of:
0,5,6,8,10 (this fails by 0-5-10, even though 6 and 8 are in the way).
So you should not be able to pick ANY three numbers from ANYWHERE in the set that create an illegal triad.
QUESTION 1: Which of the following numbers, if any, would be in the final set?
BIGGER QUESTION: There's a relatively simple way to identify the numbers that would end up in your final set. Can you identify the property/properties they all share, and find a simple way to express them?