If a solution to the problem has a "yes" answer then it WILL be found, but if it has a "NO" answer, you'll never know so because you'll keep running the algorithm in the hope of finding the "YES" answer.
Now, it turns out that in the last few months I've come across many instances of such "undecidable" problems. I'll list out a few here:
- If you have good marks on a test, you are a good student, but if you don't then it doesn't mean that you are a bad student
- If you have lots of fans on your facebook page, then you are famous but if you don't, it doesn't necessarily mean that you aren't
So, the next time I have an argument/discussion with anyone and I mention "this is undecidable", I'll try to give them a link to this post as well.