Partitioning into parts

Problem3. Can we draw a closed path made up of 9 line segments, each of which intersects exactly one of the other segments?;
Solution. If such a closed path would exist, then all the line segments could be partitioned into pairs of intersecting segments. But then the number of the segments has to be even.

Problem4.  Can a 5 by 5 square checkers board be covered by 1 by 2 dominoes?
Answer. No since we will cover even number of squares.