The seeming elegance and symmetry of the table of functions prompted me to use a technical side of my brain to ask a "what if" question about the other possible Jungian functions.
I used combinatorics(math) to calculate all possibilities of arranging letters F,S,T,N as well as adding an alternating i/e "flavor". There are two options for the flavors (once we know the i/e "flavor" of the first function, the rest are determined because they alternate).
For illustration, I enumerated one quarter of all possibilities (only those starting with an F but you can keep going yourself if you like). The original 16 types are listed below that. As you can see, there are many gaps - only 4 of 12 used here and 16 of 48 used overall. So, exactly 1/3 utilization. The mathematical elegance is a tease, makes me think that this theory is based on something real, but is it? Could it be an elegant accident or an elaborate hoax instead? Why are some combinations not possible?
E/I 1 2 3 4 functions MBTI?
e F N S T FeNiSeTi ENFJ
i F N S T FiNeSiTe INFP
e F N T S FeNiTeSi ?
i F N T S FiNeTiSe ?
e F S N T FeSiNeTi ESFJ
i F S N T FiSeNiTe ISFP
e F S T N FeSiTeNi ?
i F S T N FiSeTiNe ?
e F T N S FeTiNeSi ?
i F T N S FiTeNiSe ?
e F T S N FeTiSeNi ?
i F T S N FiTeSiNe ?
.................................
MBTI 1 2 3 4
INTP Ti Ne Si Fe
ISTP Ti Se Ni Fe
ENTP Ne Ti Fe Si
ENFP Ne Fi Te Si
ISFP Fi Se Ni Te
INFP Fi Ne Si Te
INTJ Ni Te Fi Se
INFJ Ni Fe Ti Se
ESTJ Te Si Ne Fi
ENTJ Te Ni Se Fi
ESFJ Fe Si Ne Ti
ENFJ Fe Ni Se Ti
ISTJ Si Te Fi Ne
ISFJ Si Fe Ti Ne
ESTP Se Ti Fe Ni
ESFP Se Fi Te Ni