TH-TMO 2022 Problem 6

In an examination, there are $3600$ students sitting in a $60 \times 60$ grid, where everyone is facing toward the top of the grid. After the exam, it is discovered that there are $901$ students who got infected by COVID-19. Each infected student has a spreading region, which consists of students to the left, to the right, or in the front of them. Student in spreading region of at least two students are considered a close contact. Given that no infected student sat in the spreading region of other infected student, prove that there is at least one close contact.