MHB Smallest Number Divisible by 99 Using Digits 1-9

[kaliprasad]

Find the smallest number that is made up of each of the digits 1 through 9 exactly once and is divisible by 99.

 

[Albert1]

Find the smallest number that is made up of each of the digits 1 through 9 exactly once and is divisible by 99.

my solution:

Spoiler

the smallest number that is made up of each of the digits 1 through 9 exactly once and is divisible by 99 is:
123475869
for 1+2+3+4+7+5+8+6+9=45 mod 9=0
2+4+5+6=17
1+3+7+8+9=28
28-17=11 mod 11=0
the largest number that is made up of each of the digits 1 through 9 exactly once and is divisible by 99 is:
987652413