Problem:
The average of 20 numbers is zero. How many of them may be greater than zero, at the most?

Solution:
To find the maximum number of numbers that can be greater than zero, we need to understand the concept of average and the properties of numbers.

Understanding the Average:
The average of a set of numbers is found by summing all the numbers in the set and then dividing the sum by the total number of numbers.

Properties of Numbers:
1. The sum of positive numbers is always greater than zero.
2. The sum of negative numbers is always less than zero.
3. The sum of positive and negative numbers can be zero if the sum of positive numbers equals the sum of negative numbers.

Explanation:
Given that the average of 20 numbers is zero, we can conclude that the sum of these 20 numbers is also zero.

Let's assume that there are 'x' numbers greater than zero and 'y' numbers less than or equal to zero.

Since the sum of these 20 numbers is zero, we can write the equation:
(x * positive number) + (y * non-positive number) = 0

To maximize the number of numbers greater than zero, we need to minimize the number of non-positive numbers. The smallest non-positive number is zero. Therefore, we can rewrite the equation as:
(x * positive number) + (y * 0) = 0

Simplifying the equation, we get:
x * positive number = 0

In order for this equation to be true, the value of 'x' must be zero. This means that there can be zero numbers greater than zero in the set of 20 numbers.

Therefore, the maximum number of numbers that can be greater than zero is 0.

Hence, the correct answer is option 'C' - 0.