How do you find a set of numbers that will satisfy the following conditions?

The set consists of 20 numbers. Since this is an even number of items, the median will be determined by averaging the two values in the set's center. We can make sure the median equals 24 by choosing two numbers that average to 24 (like 23 and 25) or by having both numbers equal 24.

The 20 numbers should add up to approximately 20*24 = 480, since the mean of the 20 numbers should equal about 24.

We can "space out" the min and max around a center of 24 by using the values 3 and 45 (which places each half of the range above and below). This leaves 432 - 3 - 45 = 384 for 16 numbers. If we use 24 and 24 as the innermost numbers, that leaves about 480 - 24 - 24 = 432 left for 18 numbers.

It would be nice if we could say that all 16 numbers are 24, but we're told that no more than 3 numbers are the same. Consequently, we can simply space out the numbers in pairs around 24: 23 and 25, 22 and 26, 21 and 27, 20 and 28, 19 and 29, 18 and 30, 17 and 31, and 16 and 32. It turns out that 384 is perfectly divisible by 16, resulting in 24.

This provides us with:

3, 16, 17, 18, 19; 20, 21, 22, 23; 24, 25; 26, 27, 28, 29, 30, 31, 32, and 45...

It seems like you haven't provided the conditions that need to be satisfied in order to find the set of numbers. Please provide the specific conditions or criteria that need to be met, and I'll be able to assist you in finding a set of numbers that satisfy them.