That's a huge problem when you've trying to teach them about proofs, and kicking them out of that mentality is the biggest challenge in first year under-grad. This idea of letting them work for a limited time on an unsolved problem seems a useful approach to changing their attitude.
Perhaps because they've been conditioned for 12 years to believe that this is what "math" is.
Students aren't usually taught subtraction is adding a negative number. Students aren't usually taught division is multiplying by a fraction. Students aren't usually taught that there are ways of counting outside of the decimal 'base 10' way of counting, or the advantages of counting in Octal, or how to count in Binary on your hands.
Math teachers love to say "2+2 does not always equal 4" but never explain that's only true in Base2-4 where the representation of "4" doesn't exist and it is represented as 100, 11, or 10.
So not only are we taught "there's always an answer". We're not taught other concepts and sometimes information is left out entirely until you reach a college level of mathematics - at which point all these lies, unexplained concepts, and "answer-seeking mentality" become a problem.
Learn, in my experience.
Getting people to leave a mere "answer getting" mindset and engage with the "technique and problem understanding" mindset is one of the most important parts of the job of teaching freshmen and sophomores (particularly in mathematics). They've often been rewarded for this approach in high school and have trouble letting it go -- but it really constrains the ability to understand things.
The really sad cases are the ones who are really good at it, good enough to survive all the way to grad school sometimes. They aren't doing themselves any favors, and invariably get left behind by people who may have less innate talent but engage more. Hopefully recoverably.
Thing is - it's not these kids' fault, once they do grok the notion of "not yet solved", they are great. It's that they spend the last 16 years being punished for getting something wrong, in a context where there is only a right answer or wrong answer, and that fact is known - even in subjective topics.
The focus on grades and "the right answer" instead of learning and thinking is probably why it can be so frustrating for both parties when someone fresh out of university comes to a (programming) job interview.
I've noticed a lot of attempts on freelancing sites to pay a contractor to complete homework and school assignments. I can't imagine a worse form of self-sabotage, and it seems like students have profoundly the wrong message about education.
https://news.ycombinator.com/item?id=8972744
(I don't know why you were so heavily downvoted. I upvoted you.)