I see that nines are very frequent in solutions. The reason why is because all multiples of 9 have a ** digit sum** that is a multiple of 9. For all two-digit multiples of nine except for 99, the digit sum is 9 thus making it very easy to find solutions with them. Proof is

__here__.

Chris, thank you for sharing this proof!

The 9s is a beautiful pattern, you'll also notice that you can use multiple digit sums to decompose larger multiples of 9 into 9.

For example .. the digit sum of 99 is 18. The digit sum of 18 is 9.

The same is true for all multiples of 9...

9x31 = 279... 2 + 7 + 9 = 18 … 1 + 8 = 9.

9x2435 = 21915 … 2 + 1 + 9 + 1 + 5 = 18 … 1 + 8 = 9.

9x496735 = 4470615 … 4 + 4 + 7 + 0 + 6 + 1 + 5 = 27 … 2 + 7 = 9.

Thanks