### Instruction: 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?### Response: To be divisible by 6, a number must be divisible by both 2 and 3.
To be divisible by 2, a number must end with an even digit, so the last digit of Luna's number must be either 2 or 4.
To be divisible so 3, a number must have a sum of digits that is a multiple of 3.
The sum of the digits 1, 2, 3, 4 and 5 is 15, which is already a multiple of 3, so any permutation of these digits will also have a sum of 15.
Therefore, the only condition that matters for divisibility by 6 is the last digit.
To minimize the number, we want to place the smallest digits in the leftmost positions, except for the last digit.