Rolling 6 dice

What is the probability the sum of 6 dice rolls is a multiple of 6?

Solution

This may seem at first like it requires some complicated calculations, but there is a very nice clean solution. You may find it helpful to split the problem into the sum of the first 5 dice and the value of the last die. In this case, note that for whatever the sum of the first 5 dice is, there is exactly one number we can roll for the last die that will make the sum a multiple of 6. So the probability is $1/6$. Note that this also shows that the probability is $1/6$ for any number of dice rolls.