Find the smallest number that is made up of each of the digits 1 through 9 exactly once and is divisible by 99.
A nunber is divisible by 99 if it is divisible by 9 and 11.
Divisibility rule for 9 is if all the numbers sum up to a multiple of 9, then the number is divisible by 9.
Any number made of digits 1 through 9 is divisilble by 9.
so basically the question is now:
Find the smallest number using digits 1-9 that is divisible by 11.
We start with 123456789. Because its the smallest.
Using the picture above, we get
1 + 3 + 5 + 7 + 9 = 25
2 + 4 + 6 + 8 = 20
25 - 20 = 5. Which is not divisible by 11.
So how can we manipulate the red and blue numbers to create a result that is divisble by 11?
Welp, guess and check...
Sorry, that is the best I can do. I was able to at least limit the number of guesses at least....