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

Guest Dec 29, 2019

#1**+2 **

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....

CalculatorUser Dec 30, 2019