4. In the country of Landia, which breeds an elite breed of horses, an annual festival is held to test their speed, in which only one-year-old, two-year-old, three-year-old, and four-year-old horses can participate. For each horse that meets the speed standard, the festival organizers pay a fixed amount of money to the stud farm where the horse was raised: 1 landric for a one-year-old, 2 landrics for a two-year-old, 3 landrics for a three-year-old, and 4 landrics for a four-year-old. Each stud farm participating in the festival annually enters four new horses (of any age combination as they wish) for testing, which have not previously participated in the tests, as well as personally all horses (not older than four years) that previously participated in the tests at a younger age and met the standard. What is the maximum amount of money a stud farm can earn in the first six years of its participation in the festival $\quad(12$ points)
Solution. A four-year-old horse can earn a maximum of 4 landricks over its entire participation in festivals. If the horse starts participating in festivals at 1 year old, it can participate for another 3 years after that. In the case of annual victories, it will earn $1+2+3+4=10$ landricks over 4 years. If the horse starts participating in festivals at 2 years old, it can earn a maximum of $2+3+4=9$ landricks over its 3 possible years of participation. If the horse starts participating in festivals at 3 years old, it can earn a maximum of $3+4=7$ landricks. Therefore, the most optimal strategy is as follows. In the first year, the stable enters 4 one-year-old horses. The maximum winnings are 4 landricks. In the second year, the stable enters 4 new one-year-old horses and 4 two-year-olds that participated and won in the first year. The maximum winnings are $4+4 \cdot 2=12$ landricks. In the third year, the stable enters 4 new one-year-old horses, 4 two-year-olds that participated in the second year, and 4 three-year-olds that participated in the previous 2 years. The maximum bonus is $4+4 \cdot 2+4 \cdot 3=24$ landricks. In the fourth year, there is no point in entering one-year-old horses, as they will only be able to participate for 2 more years. Therefore, it makes sense to enter 4 new two-year-old horses. The winnings will be $4 \cdot 2+4 \cdot 2+4 \cdot 3+4 \cdot 4=44$ landricks. Horses that start participating in the 5th year will only participate once after that, so it makes sense to enter new three-year-olds. The winnings will be $4 \cdot 3+4 \cdot 3+4 \cdot 3+4 \cdot 4=52$ landricks. In the sixth year,

![](https://cdn.mathpix.com/cropped/2024_05_06_58f34d7e66d046d9b7d5g-03.jpg?height=60&width=1733&top_left_y=918&top_left_x=184)
landricks. In total, over 6 years of participation in festivals, the stable can earn a maximum of $4+12+24+44+52+64=200$ landricks.

Answer: 200.