IT-CESENATICO 1991 Problem 3

We consider the sums of the form $\pm 1 \pm 4 \pm 9\pm ... \pm n^2$ . Show that every integer can be represented in this form for some $n$ . (For example, $3 = -1 + 4$ and $8 = 1-4-9+16+25-36-49+64$ .)