4. (10 points) In a cave, there is a pile of peaches, which is the common property of three monkeys. The first monkey comes to the cave, divides the peaches into two parts in a ratio of 5:4, and takes the larger part; the second monkey comes after, divides the remaining peaches into two parts in a ratio of 5:4, and takes the larger part; the remaining peaches go to the third monkey. It is known that the first monkey took 29 more peaches than the third monkey, then the second monkey took $\qquad$ peaches.
【Analysis】First, according to the problem, set the total amount of peaches as unit "1", calculate the proportion each of the three monkeys took, and then based on the fact that the first monkey took 29 more peaches than the third monkey, find out the total number of peaches, and then calculate how many peaches the second monkey took.

【Solution】Solution: According to the problem, set the pile of peaches as unit "1",
then the first monkey took $\frac{5}{9}$,
then the second monkey took: $\frac{4}{9} \times \frac{5}{9}$,
the third monkey took: $\frac{4}{9} \times \frac{4}{9}$,
then the total number of peaches: $\frac{1}{\frac{5}{9}-\frac{4}{9} \times \frac{4}{9}}=81$ (peaches),
the number of peaches the second monkey took: $81 \times \frac{4}{9} \times \frac{5}{9}=20$ (peaches)
Answer: The second monkey took 20 peaches.
Therefore, the answer is: 20 .