Odd and even

Problem5. The numbers 1 trough 10 are written in a row. Can the signs ``+'' and ``-'' be placed between them, so that the value of the resulting expression is 0?

Note that the negative numbers can also be odd or even.

Problem6. A grasshopper jumps along a line. His first jump takes 1 inch, the second 2, and so on. Each jump can take him to the right or to the left. Show that after 2001 jumps the grasshopper cannot return to the point at which he started.
Problem7.   Can one make a change of one 25 bill in ten bills with value 1,3 or 5?
Answer. No since 10 bills with value 1,3 or 5 will produce an even number.

The problem is based on a simple fact: a sum of even number of odd numbers will produce even number.