This isn't even a special interest of mine but I just really like the patterns in the first 10 multiples of 9. Most people here probably already have them memorized from school but just to help my explanation here they are:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90.
Removing the tens place it's: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
And removing the ones place it's: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
One more thing that's always made remembering them easy for me is that with 9x2 - 9x10 the tens place in each product is always one digit less than the number you're multiplying nine by. To hopefully make that make more sense:
9x2 = 1(8), 9x3= 2(7), 9x4 = 3(6), 9x5 = 4(5), 9x6 = 5(4), 9x7 = 6(3), 9x8 = 7(2), 9x9= 8(1), 9x10=9(0)
Hopefully all of that makes sense and I didn't misuse any math words :p
Yes, I know this trick and I love it ! My maths level is "almost dyscalculic", and the multiples of 9 are one of the only multiples I know because of this trick.