The 2nd International Olympiad in Informatics was held in Minsk, Byellorussia, in 1990. There were two competition rounds, and you can see all problems below (divided by rounds, i.e. Round 1 and Round 2).

Problems:
      Round 1
      Round 2

Note that the grading model changed at IOI'94 and beyond.
Before IOI 1994, a human evaluator would sit behind the competitor's computer and do the testing manually (enter test data through the keyboard, check the output on the screen). Starting from IOI 1994, an automatic grading process is used, with test input defined in files.