How many 20-digit numbers are such that the sum of their digits is even?

The first 20-digit number is 10,000,000,000,000,000,000

The last 20-digit number is 99,999,999,999,999,999,999

The total number of 20 digit number is: 90,000,000,000,000,000,000.

The sum of the digits of 10,000,000,000,000,000,000 is odd.

The sum of the digits of the next number will be even, next odd, and so on.

Then, half of the numbers will give an even result and half an odd result.

Answer: 90,000,000,000,000,000,000 / 2 = 45,000,000,000,000,000,000 20-digit numbers. That is 45 * 10^18 numbers.