Question

Using no digits other than 5 and 8, make a 6-digit number, that has the properties below. If it is impossible, write so. Of course you may use each digit more than once. A multiple of 24.

Answer 1

Since it's a multiple of 24, it has to be a multiple of the factors of 24.

Factors of 24:
2,3,4,6,8,12

You can use some of this knowledge to help create the number.
Since the # needs to be a multiple off 2, the last digit needs to be an 8

All numbers that are multiples of 3 have the property that all of their digits added together have to be a number that is evenly divisible by 3.

so your number will look like:
_ _ _ _ _ 8

so start trying combinations for the other 5 digits that give you a number that is a multiple of 3: 3,6,9,12,15, ect. If you can't find one, then it's impossible