Luna writes down all the five-digit numbers that contain each of the digits 1, 2, 3, 4 and 5 exactly once. What is the smallest number in Luna's list that is divisible by 6?

Question

mathstudent55 · Answer

Do you know the divisibility test for 6?

mathstudent55 · Answer

A number is divisible by 6 if it is divisible by both 2 and 3.
A number is divisible by 2 if is is even.
A number is divisible by 3 if the sum of its digits is divisible by 3.

mathstudent55 · Answer

If the 5-digit number contains one each of the digits 1, 2, 3, 4, and 5, then make sure such a number is divisible by 3. 
What is the sum of 1, 2, 3, 4, and 5?

mathstudent55 · Answer

Are you still there?

mathstudent55 · Answer

I have to go.
This is what you need to do.
1. Make sure the number is divisible by 3.
2. If it is divisible by 3, then choose the smallest even number you can make by using those 5 digits.
The way to accomplish this is to write the digits starting with the smallest digit, then the next bigger one, etc. If you continue this way, the number will end with 5 and won't be even, so at the end, switch the last two digits, so you end up with an even digit at the end and the smallest possible even number.