Umeko1.0

The solids both have a surface area of

 \(1*6=6\)

if you add 6 times 2, you get 12. 12-2=10

This is pretty simple. NotThatSmart already showed one way. If you know your primes, you'll find 2, 3, 5, and 7 to be prime. 

The answer is 30 ways.

You have 6 ways for the first bead, then 5 for the next. If we have already used the colored beads, then we have 1 for all the rest.

6x5=30.

There really isn't a direct explanation for this, but I'll try my best. Say 0.x repeating is a decimal, and you want to convert it to a fraction. First, name that value n and name 10 times that value 10n. Equation below:

 n = 0.xx...

10n = x.xx...

{Minus n from both sides}

 9n = x

 n = x/9