I count more than 3 shapes 
Once you start using triads to make music it becames just like remembering open or barre chords or more like arpeggios if you use them in solos. You’ll find favorate shapes first then you’ll find convenient shapes the go together with your favorates. Using your ear to find chord tone will come next the you won’t think about it you’ll just find yourself playing what sounds good.
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I think Shane means 3 shapes per string set.
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Have you guys heard of the Plane Talk method by Kirk Lorange? He advocates only learning the three shapes in the green box. They are all second inversion. The advantage of only remembering these three is you always flatten the thinnest string in the group one fret to make the chord minor. Raise the same note one fret and you have a sus 4. Flatten the root and you get a major7 sound. Flatten the root again and you get a dom7 sound.
You’ll find you’re jumping all over the neck only using 1 shape per string set and soon be learning the rest. Or you’ll find you never or hardly ever use triads in your playing.
I think Justins method of mastering the 3 shapes per string set together then move to the next string set is a better way to learn them.
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Perhaps to clarify the 3 basic ‘shapes’, as I see them.
EAD strings - the 3 basic shapes.
ADG strings - exact same 3 shapes
DGB strings - same 3 ‘shapes’ again, just accommodating the B string tuning
GBE - same 3 ‘shapes’ again, just accommodating B string tuning.
Obviously, there are more than 3 actual visual shapes
Functionally though, there are only 3 basic shapes.
To illustrate, play a root position C major triad.
Start on the bottom 3 strings. So CEG
Drop to the next string (A) , play CEG. Same shape.
Drop to the next string (D) , play CEG. Same shape again, except the G note moves up a fret on the B string.
Drop to the next string, play CEG. Same shape again, except now both notes (E and G) are moved up one fret on the B and e strings respectively.
Play the 2 inversions as per above, and you have the other 2 basic shapes.
Cheers, Shane.
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True, knowing all the shapes does facilitate less movement.
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I hope I’m stating the obvious, but these are also subsets of the E-, A- and D-shape major barre chord grips. For beginners, this might be more tangible than all of them being 2nd inversions.
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