It is absolutely NOT a trick question.

There are an infinite number of hypotheses for what an 'Awesome Triplet' could be. Here are some example hypotheses that could be true based on our initial evidence '2 4 6 is an awesome triplet':
1. Any three integers
2. Any three integers in ascending order
3. Three successive multiples of the same number
4. The sequence '2 4 6'
5. Three integers not contained in the set '512 231123 691 9834 91238 1'

We cannot falsify every possible hypothesis, so we need a strategy to falsify hypotheses, starting from the most likely. All hypotheses are not created equal.

I want to falsify as much of the hypotheses-space as possible (where simple hypthoses take up more space), so I design a test that should do so. My first test was '3 integers in descending order', because it can falsify #1, the simplest hypothesis. I find from this test that #1 is false. My second test is to distinguish between #2 & #3; '3 integers in ascending order, but not successive multiples of the same number', '1 2 5' I find from this test that #2 is still plausible, but #3 is falsified.

You can continue falsifying smaller and smaller areas of the hypothesis-space with additional tests, up until you're happy with your confidence level or you're bored of testing.

For much better coverage of this entire area, see the following posts by Eliezer:
* What is Evidence?
* The Lens That Sees Its Flaws
* How Much Evidence Does It Take?
* Occam's Razor

For a good overview of additional related posts, see the list.

Edit: Learning Markdown, fixing style.