johnsparkly251 describes how to reach all 50 answers as such:
"4+4-4-4 = 0
(4+4)÷(4+4) = 1
(4÷4)+(4÷4)=2
(4+4+4)÷4=3
4! - ((4×4)+4) = 4
((4-4)4)!+4 = 5
((4+4)÷4)+4 = 6
(4+4)-(4÷4) = 7
4+4-4+4 = 8
4+4+(4÷4) = 9
(44-4)÷4 = 10
((4!+4)÷4)+4 = 11
4!-((4×4)-4) = 12
(4!+4!+4)÷4 = 13
(4!÷4)+4+4 = 14
(4×4)-(4÷4) = 15
4+4+4+4 = 16
(4×4)+(4÷4) = 17
(4!+4!+4!)÷4 = 18
4!-(4-4)!-4 = 19
4!-4+4-4 = 20
4!+(4-4)!-4 = 21
(4!÷4)+(4×4) = 22
4!-((4-4)4)! = 23
(4×4)+4+4 = 24
4!+((4-4)4)! = 25
4!+((4+4)÷4) = 26
4!-(4-4)!+4 = 27
4!-4+4+4 = 28
4!+(4-4)!+4 = 29
(4+4+4)÷.4 = 30
((4!+4)÷4)+4! = 31
(4×4)+(4×4) = 32
(4-.4)÷.4+4! = 33
44-(4/.4) = 34
(44/4)+4! = 35
4!+4+4+4 = 36
((√4+4!)/√4)+4! = 37
44-(4!/4) = 38
((4×4)-.4)/.4 = 39
4!+4!-4-4 = 40
(4×4+.4)/.4 = 41
4!+4!-(4!÷4) = 42
44-(4÷4) = 43
44-4+4 = 44
44+(4÷4) = 45
44-√4+4 = 46
4!+4!-(4÷4) = 47
4!+4!+4-4 = 48
4!+4!+(4÷4) = 49
44+(4!÷4) = 50."
BONUS PUZZLE: By the way, we can actually also reach all the way up to 72 if we throw in a new symbol to play with: %. Can you now find them all?
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Alternatively
44-44=0, 44/44=1, & 44÷4+sqrt4=13 also work
As for 51 to 72
(4!-4+.4)÷.4=51
(4!+sqrt4)×4÷sqrt4=52
4!×sqrt4+4+sqrt4=54
44÷sqrt4÷.4=55
4!+4!+4+4=56
4!÷.4-4+sqrt4=58
4!÷.4-(4÷4)=59
4×4×4-4=60
4!÷.4+(4÷4)=61
4×4×4-sqrt4=62
4!+44-4=64
4×4×4+sqrt4=66
4×4×4+4=68
44+4!+sqrt4=70
(4!+4.4)÷.4=71
(4!×4!)÷(4+4)=72
All equations follow BEDMAS
sqrt means the square root
Only missing 53,57,63,65,67
Let me help you with that:
4!*√4+√4/.4=53
(4!-√4)/.4+√4=57
(4!+√4)/.4-√4=63
4!/.4+√4/.4=65
(4!+√4)/.4+√4=67