Speed is the Key!

Lets look at the multiplications of 9 (that special number!) :

9 X 1 = 09
9 X 2 = 18
9 X 3 = 27
9 X 4 = 36
9 X 5 = 45
9 X 6 = 54
9 X 7 = 63
9 X 8 = 72
9 X 9 = 81
9 X 10 = 90

If you look closely, the product of the multiplication seem to follow a simple pattern. And if you are familiar with the concept of "Digital Sum", you will also notice something else. What?

First of all, if you look at the first result, (I have deliberately written it as 09 rather than just 9), you will notice that the Digital Sum of the the result is also 9. This is the same for all the multiplications of nine. So this is our first clue.

Secondly, when 9 is multiplied by a number (up to 10, in the first set), the result then starts with a number that is one less. Say for instance, 9 X 6, the result must start with a number one less than 6, which is 5. And since we know that the Digital Sum of the result must be also 9, so the second number must be....4, of course! So the answer is simply 54.

Simple isn't it?

Expanding if further, notice that any product of multiplications of 9 has a Digital Sum of 9: e.g.:

108 X 9 = 972

972 --> 9+7+2 --> 18 --> 1+8 --> 9!