5.3. In a seven-story building, domovoi (Russian house spirits) live. The elevator travels between the first and the last floors, stopping at every floor. On each floor, starting from the first, one domovoi entered the elevator, but no one exited. When the thousandth domovoi entered the elevator, it stopped. On which floor did this happen? Explain your answer.
Answer: on the fourth floor.

Solution. First, let's find out how many housekeepers ended up in the elevator after the first trip from the first to the seventh floor and back, until the elevator returned to the first floor. One housekeeper entered on the first and seventh floors, and on all other floors, two housekeepers entered. Thus, in one such trip, 12 housekeepers ended up in the elevator.

Now, let's find out how many such complete trips the elevator managed to make. When dividing 1000 by 12, the quotient is 83 and the remainder is 4. This means that after 83 ascents and descents, 4 more housekeepers can still enter the elevator: on the first, second, third, and fourth floors.

## Grading criteria:

+ correct answer and a fully justified solution

$\pm$ correct answer and a generally correct solution, but there are gaps and deficiencies in the justification

干 correct answer only

干 correct answer is missing, but the correct idea of dividing the elevator trips into "cycles" of 12 housekeepers is indicated

- the problem is not solved or solved incorrectly

(Note: The "干" characters in the grading criteria should be replaced with appropriate English terms, such as "partially correct" or "incomplete.")