Tuit,tui & tut are the root-words for many other words.
These ROOT-WORDS are TUT, TUIT & TUI which come from the Latin tueri & tuitus which mean TO PROTECT & TO GUARD and from that comes the meaning TO TEACH. With the addition of the Prefix IN which, as you know, means NOT, a new concept comes into the word, INTUITion, learning without instruction. How wonderful it would be to get all knowledge by INTUITion! If the multiplication tables were in TUITable?
1.	Tutor	:	TUT or (tute' or) n.
2.	Tutoress	:	TUT oress (tute' o res) n.
3.	Tutorly	:	TUT orly (tue' tor li) adv.
4.	Tutorage	:	TUT orage (ture' o rij) n.
5.	Tutorial	:	TUT orial (tue tore' ee al) adj.
6.	Tutoriate	:	TUT oriate (tue toe' ri at) n.
7.	Tuition	:	TUI tion (tu ish' un) n.
8.	Intuit	:	in TUIT (in tue' it) v.
9.	Tuitional	:	TUIT ional (tu ish' un al) adj.
10.	Intuition	:	in TUIT ion (in tuish' un) n.
11.	Intuent	:	in TU ent (in' tue ent) adj.
12.	Intutitable	:	in TUIT able (in tue' it a b'l) adj.
13.	Intuicity	:	in TUI city (in tu is' i ti) n.
14.	Intuitive	:	in TUIT ive (in tue' it iv) adj.
15.	Intuitively	:	in TUIT ively (in tue' it iv lee) adv.
16.	Intutionism	:	in TUIT ionism (in tue ish' u niz um) n.
17.	Intuitionist	:	in TUIT ionist (in tue ish' u nist) n.
18.	Intuitivism	:	in TUIT ivism (in tue' i tiv iz um) n.