23rd All Soviet Union Mathematical Olympiad Problems 1989

1.  7 boys each went to a shop 3 times. Each pair met at the shop. Show that 3 must have been in the shop at the same time. 2.  Can 77 blocks each 3 x 3 x 1 be assembled to form a 7 x 9 x 11 block? 3.  The incircle of ABC touches AB at M. N is any point on the segment BC. Show that the incircles of AMN, BMN, ACN have a common tangent. 4.  A positive integer n has