Thursday, November 11, 2010
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
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