I can’t play Ashape barre 7th chords so this is what I’ve done to get a C#7 chord for the song I’m learning:
Can I call it a Jumbled triad? It sounds very similar to the 7th Ashape
maybe I would call that an “inversion”…there’s the 7th, it’s 4 notes not 3! 
ooops 
Yep, 7th chords are extensions and are not triads, unless you omit the 5th (which you didn’t). If I followed your method correctly, the bass note of your grip is an F on string 4 (string 5 is not played). Since F is the 3rd, it’s a first inversion grip.
Thank you Jozsef 
There! Sometimes I miss terms 
You can always call them four-note chords as well 
or quadads, as Justin refers to them.
Root Chord - 1 3 5 - C E G
1st Inversion - 3 5 1 - E G C
2nd Inversion - 5 1 3 - G C E
I had no problem with the test. What I don’t understand is why is there no 5 3 1 - G E C and 1 5 3 - C G E and 3 1 5 E C G
Take a good look at your fret board. You’ll notice the note E is either on the same string as the note G or 4 frets up on the next string. same goes for the E and C the note C is on the same string or 3 frets up on the next string. So not very playable and there are better and easier shapes.
This should stop you from exploring these shape for soloing sliding into chord tone from another chord to is totally doable and sound good.
Thanks @stitch, you confirmed my guess! I’m guessing this playability issue generalizes to any instrument that is capable of playing chords: I suspect those stretches would be pretty challenging on a keyboard as well.
A key board is a little different. You can play every note ahead or behind any other note but on stringed instruments you cant play two notes on the same string at the same time even if you use both hands.
If you look at the fret board(in standard tuning) on a guitar the interval fall in a specific pattern(except on the B string) the root is always under the 5th and the 3rd is always 1 back and under the root. This is why chords and triad are the way they are.
Hmm. Does this imply that this discussion of triads and inversions is specific to guitar? As I (slowly and intermittently) learn theory, I hope to understand what is “general” theory, and what discussions are specific to an instrument.
I don’t know, I’ve never studied theory until I found Justin’s website and the reason Justin started the PMT course was to clarify what theory applies to guitar. I’m guessing inversions would apply the same to piano because the notes are in the same order so the first inversion would start with the 3rd and the second inversion would start with the 5th.
On a piano you could also play any of the note more than an octave apart but I’m not sure if that is still classified as a triad. It may just be an arpeggio.
But not inversions. the biggest difference between a guitar and piano is on a piano every triad/chord is different for each of the 12 notes. Meaning 12 different shapes + invesions.
On a guitar all the chords/scales etc are the same using only 5 shapes for chords and 3 shapes for triads.
Does this shed any light?
Thanks James @Socio, that article does confirm that the three ways of playing a triad are consistent between guitar and piano:
Since they contain three notes, you can play triads in three different ways, known as root position, first inversion and second inversion.
Hopefully someone can address Roland’s original question (or confirm Rick’s @stitch observation that these other orderings are difficult to play):
Edited to reference prior posts in this topic @Rolandson, there is a discussion of just what you ask way up at the top of this topic, beginning with post 5. I haven’t had time to digest it yet myself, but hopefully it will make things clear to you!
Thank you.
Found it.
These are possible, but not on adjacent string sets.
See the last section of this post above: Chord Inversions & Jumbled Triads - #20 by Richard_close2u
Yes thank you. This gave me the answer.