▪ Kosovo Team Selection Tests 2012

1. A student had papers. He seleced some of these papers, then he cut each of them in pieces.He took these pieces and selected some of them, which he again cut in pieces each.The student took this procedure untill he got tired .After a time he counted the pieces and got pieces .Prove that the student was wrong during the counting. 

2. Find all three digit numbers, for which the sum of squares of each digit is . 

3. If are the sides of a triangle and are the medians prove that

4. Each term in a sequence starting with the seventh is the sum of the last 6 terms mod 10 .Prove that the sequence never occurs 

5 Prove that the equation 

has infinitly many natural solutions.