Problem 3.5. Vanya wrote the number 1347 on the board.

- Look! - noticed Petya. - In this number, each of the last two digits is equal to the sum of the two preceding ones.
- Exactly! - agreed Vasya.
- Can you write the largest four-digit number like this?

Help Vasya complete Petya's task.
Answer: 9099.

Solution. It is clear that in the number 9099, each of the two last digits is equal to the sum of the two preceding ones.

If there existed a four-digit number with such a property that was even larger, then its first digit would be 9, and the second digit would be no less than 1. But then the third digit would be no less than $9+1=10$, which is impossible.