I went to interview to CS Center. The interview consists of two parts, 30 minutes each.

In the first part they give you 3 problems. I had folllowing problems:
1) How many ways to make a tower of height N from red and blue cubes so that not a single red would stand on red.
I didn't have time to solve this problem at the interview, but solved it later. In the comments I will give a hint and then a solution
2) Write code that finds an element in an array that occurs in more than half of the positions. Time: O(n) Memory: O(1)
I solved it, the solution will be in the comments
3) A boring task with equations and graphs, I solved it

In the second part you tell about your motivation, how good you are, and how much free time you have
I hope I will pass (but don't believe it)