Question 77
The commuter village of Abelia has a population of $2022$ individuals. Households vary but the average household size is $3$ people. Houses are numbered consecutively.
Every inhabitant of Abelia takes a return train trip to a nearby city. There are four trains from Abelia to the city in the morning and four trains from the city to Abelia in the evening.
Show that there are two individuals who were on the same train both in the morning and in the evening, and whose house numbers differ by at most $5$.
Every inhabitant of Abelia takes a return train trip to a nearby city. There are four trains from Abelia to the city in the morning and four trains from the city to Abelia in the evening.
Show that there are two individuals who were on the same train both in the morning and in the evening, and whose house numbers differ by at most $5$.