Problem 4.3. Sasha had 47 sticks. Using them all, he formed several letters "B" and "V" as shown in the figure. What is the maximum number of letters "B" that Sasha could have formed?
![](https://cdn.mathpix.com/cropped/2024_05_06_c60160c61c72db74c711g-2.jpg?height=302&width=542&top_left_y=264&top_left_x=448)
Answer: 8.

Solution. To form the letter "Б", 4 sticks are needed, and to form the letter "В", 5 sticks are needed.

- Sasha could not have formed at least 12 letters "Б" because it would require no less than 48 sticks.
- If Sasha had formed 11 letters "Б", he would have $47-11 \cdot 4=3$ sticks left. This would not be enough even for one letter "В".
- If Sasha had formed 10 letters "Б", he would have $47-10 \cdot 4=7$ sticks left. One letter "В" could be formed, but there would be extra sticks left.
- If Sasha had formed 9 letters "Б", he would have $47-9 \cdot 4=11$ sticks left. Two letters "В" could be formed, but there would be one extra stick left.
- If Sasha had formed 8 letters "Б", he would have $47-8 \cdot 4=15$ sticks left. This is exactly enough for 3 letters "В".