Let’s break it down step by step:

What does it mean that the average of 20 numbers is zero?

When we calculate the average, we add up all the numbers and divide by how many numbers there are. In this case, we have 20 numbers. If their average is zero, it means that:

20 numbers added together = 0

What does this tell us about the sum of the numbers?

Since the average is zero, the sum of all 20 numbers must also be zero. Think of it like a seesaw: if some numbers are positive (above zero), others must be negative (below zero) to balance them out.

How can we maximize the number of positive numbers?

To have as many positive numbers as possible, we want the negative numbers to be as small as possible (just less than zero). This way, we can have more positive numbers to balance them out.

The most extreme case

Imagine we have 19 very small positive numbers, and 1 very large negative number. The large negative number could balance out the sum of the 19 positive numbers, making the total sum zero.

Conclusion

In the most extreme case, we can have 19 numbers greater than zero. This is because we can balance them out with 1 large negative number.

So, to answer the question: at most, 19 numbers can be greater than zero.