Find all pandigital sums of the form

abc+def=ghi

(with no zero) in ascending order of ghi and find a pattern in these sums.

Pattern aside, all pandigital sums must be evenly divisible by 9.

This is because x + y + z = 0 mod 9 if all digits 1-9 are represented in x, y and z exactly once.

But if x + y = z mod 9,

then x + y - z = 0 mod 9,

so 2z = 0 mod 9,

so z = 0 mod 9.

*Edited on ***June 28, 2016, 8:11 pm**