20. (6 points) If the ten-digit number $\mathrm{a} 2016 \mathrm{~b} 2017$ is divisible by 33, then, how many such ten-digit numbers are there?
【Solution】Solution: According to the tens digit that can be divided by 33, it can be divided by 3 and 11.
The sum of the digits is $a+2+0+1+6+b+2+0+1+7=19+a+b$ which is a multiple of 3.
The difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11. $7+0+b+1+2-1-2-6-0-a=b+1-a$ is a multiple of 11.

When $b+1-a=0$, $a-b=1$, $a+b$ can be $5,11,17$ so $a=3, b=2$ satisfies the condition. $a=6, b$ $=5$ satisfies the condition. $a=9, b=8$ satisfies the condition.

There are a total of 3 solutions that meet the conditions.
Therefore, the answer is: 3.