3rd Brazilian Mathematical Olympiad Problems 1981

3rd Brazilian Mathematical Olympiad Problems 19811.  For which k does the system x2 - y2 = 0, (x-k)2 + y2 = 1 have exactly (1) two, (2) three real solutions? 2.  Show that there are at least 3 and at most 4 powers of 2 with m digits. For which m are there 4?