This is not my homework, this is for my recreation and hope you people could solve my trouble.
I have each of ordered sets (x,y) in which x and y equal to a integer from 1 to 5 respectively in which every set have a different x from each set and a different y from each set. I arrange the y number to be from small to big, that is the sequence looks like this:$(x_1,1),(x_2,2),(x_3,3),(x_4,4),(x_5,5)$, and then i want to rearrange those same sets a few time between two set each time in which x will be in a "correct place" to make it become a sequence that looks like:$(1,y_1),(2,y_2),(3,y_3),(4,y_4),(5,y,5)$ for which each x is in correct place now and the rule is we have to make at least one x into "correct place" for each rearrangement. Finally, i get a number $(-1)^p$ for which p is the rearrangement required for the originl sequence to became the "correct place" sequence.
Second of all, i create a chart in ordered that look like this:
1 2 3 4 5
for which i connect each number of 1, 2, 3, 4, 5 to a corresponding y to a number that is equal to the y, then i count the number of the intersection of the line which only two line intersect at a point, then for i equal to the intersection number, i compute this number: $(-1)^i$,