TopsOJ Summer 2025 - Guts Round - Problem 14

A room initially has n people. Three observers make the following remarks:

• After 5 people leave, Observer 1 says “the room has 90\% of its original number of people.”
• After 10 more people leave, Observer 2 says “the room is 80\% as full as when Observer 1 made his remark.”
• After 5 more people leave, Observer 3 says “the number of people dropped by \frac17 from when Observer 2 made his remark.”

One observer is wrong. What is the sum of the incorrect observer's number and n?