This weekend I have IOI team selection tests, I should be able to get on the team, but I am still afraid because, if I'll fail a single problem there are these lower grade contestants who just suck out points off the problems without solving them ( We have outdated judge with no subtasks and partial points :/ ). I believe my main problem is that I often come up with wrong solutions, and I struggle hour or two until I find wrong case for it. Any tips how to avoid these type of problem? Is it right to always prove solution before typing? And on the other hand how do you spend last week/days before important contests?

BTW. I'm from Republic of Georgia.