Question 5
Suppose $N_1,N_2,\ldots,N_{2011}$ are positive integers. Let
$$X=(N_1+N_2+\cdots+N_{2010})(N_2+N_3+\cdots+N_{2011}),$$
$$Y=(N_1+N_2+\cdots+N_{2011})(N_2+N_3+\cdots+N_{2010}).$$
Which one of the following relationships always holds?
$$X=(N_1+N_2+\cdots+N_{2010})(N_2+N_3+\cdots+N_{2011}),$$
$$Y=(N_1+N_2+\cdots+N_{2011})(N_2+N_3+\cdots+N_{2010}).$$
Which one of the following relationships always holds?