Now that we've put in some hard work into our system, we can already start to see some rewards. Let's say someone says, play all the C's on the guitar. At first this might seem quite daunting, but we can first just remember that C is 0*, and that our tuning tells us that the open strings are: 4* 9* 2* 7* 0* 5*.
Since we know that if we move up the neck (where up means towards the center of the guitar since that makes the pitch go up) that that increases the pitch by 1. So the first fret on the 4* string is 5*, and the n-th fret on the 7* string is 7* + n. Due to this we can now start to find all the C's on the guitar.
On the 4* string, we can see that by adding 8 to 4* we end up with 0*, so the 8th fret on the 4* is where one C is.
Moving to the 9* string, 9* + 3 = 0* so it's 3rd fret on the 9* string.
With the 2* string, we have 2* + 10 = 0*, so 10th fret works.
On the 7* string, 7* + 5 = 0* so 5th fret.
On the 0* string, we don't have to do anything, we can play that string with no fretting.
On the 5* string, 5* + 7 = 0* so 7th fret.
In general given the string S*, and the note N*, the fret which you can get the note N* is I(S*, N*) or just N - S.
So without any muscle memory on the guitar, we've been able to locate all C's on the guitar, this method will work for any note.