Htydjtk

Rules

Use ALL the digits in the year $2019$ (you may not use any other numbers except $2, 0, 1, 9$) to write mathematical expressions that give results for the numbers 50 to 100.

You may use the arithmetic operations $+$, $-$, $times$, $sqrt{}$, and $!$ (see below).
Indices or exponents may only be made from the digits $2, 0, 1,$ and $9$; for example, $(9+1)^2 $is allowed, as it has used the $9$, $1$ and $2$. Multi-digit numbers and decimals points can be used such as $20$, $102$, and $.02$, but you CANNOT make 30 by combining $(2+1)0$.

Recurring decimals can be used using the overhead dots or bar e.g. $0.bar1=0.111 ...=frac19$

Factorials are allowed

Here's how you might use factorials:

$n!=ntimes(n-1)times(n-2)timesdotstimes2times1$

For example
$(10-9+2)!=3!=3times2times1=6$
$0!=1$

Here are answers for all numbers. I'm going to try to find better answers for 76 and 86 because not only is it dumb trying to read multifactorials, but Wolfram Alpha can't even calculate anything past double factorials.

50: $10 * (sqrt9 + 2)$

51: $((sqrt9)!)!! + 2 + 1 + 0$

52: $((sqrt9)!)!! + 2 + 1 + 0!$

53: $9 * (2 + 1)! - 0!$

54: $9 * (2 + 1)! + 0$

55: $9 * (2 + 1)! + 0!$

56: $((sqrt9)!)!! + (2 + 1 + 0!)!!$

57: $19 * (2 + 0!)$

58: $10 * (sqrt9)! - 2$

59: $20 * sqrt9 - 1$

60: $20 * sqrt9 * 1$

61: $20 * sqrt9 + 1$

62: $10 * (sqrt9)! + 2$

63: $21 * sqrt9 + 0$

64: $(9 - 1)^2 + 0$

65: $2^{(sqrt9)!} + 1 + 0$

66: $2^{(sqrt9)!} + 1 + 0!$

67: $((sqrt9)!)!! + 20 - 1$

68: $((sqrt9)!)!! + 21 - 0!$

69: $90 - 21$

70: $10 * (9 - 2)$

71: $91 - 20$

72: $12 * (sqrt9)! + 0$

73: $12 * (sqrt9)! + 0!$

74: $((sqrt9)!)! * .1 + 2 + 0$

75: $((sqrt9)!)! * .1 + 2 + 0!$

76: $21!!!!!!!!!!!!!!!!! - 9 + 0!$

77: $((sqrt9)!)! * (.bar1) - 2 - 0!$

78: $90 - 12$

79: $9^2 - 1 - 0!$

80: $9^2 - 1 + 0$

81: $9^2 + (1 * 0)$

82: $9^2 + 1 + 0$

83: $9^2 + 1 + 0!$

84: $90 - (2 + 1)!$

85: $91 - (2 + 0!)!$

86: $(20 - 1)!!!!!!!!!!!!!! - 9$

87: $90 - 2 - 1$

88: $90 - (2 * 1)$

89: $90 - 2 + 1$

90: $92 - 1 - 0!$

91: $91 + (2 * 0)$

92: $92 + (1 * 0)$

93: $92 + 1 + 0$

94: $92 + 1 + 0!$

95: $((sqrt9)!)!! * 2 - 1 + 0$

96: $90 + (2 + 1)!$

97: $91 + (2 + 0!)!$

98: $((sqrt9)!)!! * 2 + 1 + 0!$

99: $(9 + 1)^2 - 0!$

100: $(9 + 1)^2 + 0$

Here are two more solutions:

67 = $((sqrt 9)!)!! + 20 - 1$

68 = $((sqrt 9)!)!! + 21 - 0!$

some solutions without double factorials

51:

$ .02^{-1} + .bar9 $

52:

$ (sqrt9)! * (.bar1)^{-0!} - 2 $

56:

$ .02^{-1} + (sqrt9)! $

67:

$ ((sqrt9)!)! * .1 - .2^{-0!} $

76:

$ .bar1^{-2} - (sqrt9)! + 0! $

86:

$ 91 - .2^{-0!} $

95:

$ 19 * .2^{-0!} $

98:

$ .1^{-2} + 0! - sqrt9 $

Hope few of my solutions (not mentioned before) will help you. It's not an easy task and I'm curious if it's even possible to come up with each of them.

54:

$54 = 9*1*(2+0!)!$

64:

$64 = (9-1)^2+0$

71:

$71 = 91 - 20$

76:

$76 = 19 * (2 + 1 + 0!)$

81:

$81 = sqrt{9}^{(2^{(0!+1)})}$

82:

$82 = 92 - 10$

95:

$95 = 190 / 2$

99:

$99 = (9+1)-0!$