9. Find the number of natural numbers from 1 to 100 that have exactly four natural divisors, at least three of which do not exceed 10.
Answer: 8.

Solution: A number has exactly 4 natural divisors if it is either the cube of a prime number or the product of two prime numbers. The cubes of prime numbers (satisfying the conditions) are: 8 and 27. Prime numbers not greater than 10 are - 2, 3, 5, and 7. All their pairwise products satisfy the conditions, and their number is 6.