[niko]

How many ways are there of rolling three 6's with one die, where X is the number of rolls.

[reinsuranc]

In 1 roll, there are no ways this can be done.
In 2 rolls there are no way this can be done.
In 3 rolls, there is only one way this can be done.

[CroCivic91]

If X is smaller than 3, you cannot roll 3 6s with X rolls.

If X is larger than 3, you can think of this problem like this:

Imagine you code throws like this:

"O" - you rolled a 6
"I" - you rolled something other than a 6

So, if X = 4, one output can be OIII, which means you first rolled a 6, and then 3 times you rolled something other than 6.

Your original question can now be formed like this: how many "sequences of letters 'O' and 'I'" are there that are X letters long and have 3 'O's in it?

Basically, you need to pick out 3 positions in the "sequence" and place 'O's there, and fill the rest with 'I's. So there are "X over 3 (binom coefficient)" ways to do that.

For example, if X is 3, there is "3 over 3 = 1" way of doing it. For X = 4, there are "4 over 3 = 4 over 1 = 4" ways of doing it. They are "OOOI", "OOIO", "OIOO" and "IOOO".

Hopefully this is correct. Sure sounds logical to me.