1984 AIME Problem 10

Mary told John her score on the American High School Mathematics Examination (AHSME), which was over 80. From this, John was able to determine the number of problems Mary solved correctly. If Mary’s score had been any lower, but still over 80, John could not have determined this. What was Mary’s score? (Recall that the AHSME consists of 30 multiple-choice problems and that one’s score, $s$, is computed by the formula $s = 30 + 4c - w$, where $c$ is the number of correct and $w$ is the number of wrong answers; students are not penalized for problems left unanswered.)

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.