All 100 targets have a solution.
\(1 = \frac{ 18 - 9 }{ 9 }\)
\(2 = 91 - 89 \)
\(3 = \frac{ 18 + 9 }{ 9 }\)
\(4 = \frac{ 8 }{ \frac{ 9 }{ 9 } + 1 }\)
\(5 = \frac{ 18 }{ 9 } + \sqrt{9 }\)
\(6 = \frac{ 18 }{ 9 } \cdot \sqrt{9 }\)
\(7 = 98 - 91 \)
\(8 = \frac{ 81 - 9 }{ 9 }\)
\(9 = \sqrt{99 - 18 }\)
\(10 = \frac{ 81 + 9 }{ 9 }\)
\(11 = \frac{ 99 }{ \sqrt{81 } }\)
\(12 = \sqrt{18 - 9} + 9 \)
\(13 = 1^{8} + \sqrt{9} + 9 \)
\(14 = 19 - 8 + \sqrt{9 }\)
\(15 = \frac{ 18 }{ \sqrt{9} } + 9 \)
\(16 = 8 - 1^{9} + 9 \)
\(17 = 18 - \frac{ 9 }{ 9 }\)
\(18 = 99 - 81 \)
\(19 = \frac{ 9 }{ 9 } + 18 \)
\(20 = 19 - 8 + 9 \)
\(21 = \frac{ 189 }{ 9 }\)
\(22 = \frac{ 198 }{ 9 }\)
\(23 = ( 1 + \sqrt{9} ) \cdot 8 - 9 \)
\(24 = 18 - \sqrt{9} + 9 \)
\(25 = 8 - 1 + 9 + 9 \)
\(26 = 1 \cdot 8 + 9 + 9 \)
\(27 = \sqrt{18 - 9} \cdot 9 \)
\(28 = \sqrt{( 9 - 1 ) \cdot 98 }\)
\(29 = 8 \cdot \sqrt{9}! - 19 \)
\(30 = \sqrt{891 + 9 }\)
\(31 = \frac{ \sqrt{9}!! }{ 18 } - 9 \)
\(32 = \sqrt{19 - \sqrt{9}} \cdot 8 \)
\(33 = \frac{ 198 }{ \sqrt{9 }! }\)
\(34 = 8 \cdot \sqrt{9} + 1 + 9 \)
\(35 = 1 \cdot \sqrt{9} \cdot 9 + 8 \)
\(36 = 18 + 9 + 9 \)
\(37 = ( \sqrt{9}! - 1 ) \cdot 9 - 8 \)
\(38 = ( 8 - \sqrt{9}! ) \cdot 19 \)
\(39 = 1 \cdot 8 \cdot \sqrt{9}! - 9 \)
\(40 = \frac{ ( 9 - \sqrt{9} )! }{ 18 }\)
\(41 = ( 1 + \sqrt{9} ) \cdot 8 + 9 \)
\(42 = ( 8 - 1 ) \cdot ( 9 - \sqrt{9 } )\)
\(43 = 8 \cdot \sqrt{9} + 19 \)
\(44 = ( 1 + \sqrt{9} ) \cdot 9 + 8 \)
\(45 = 18 \cdot \sqrt{9} - 9 \)
\(46 = ( 8 - \sqrt{9} ) \cdot 9 + 1 \)
\(47 = ( 9 - \sqrt{9} ) \cdot 8 - 1 \)
\(48 = ( 8 - 1 + 9 ) \cdot \sqrt{9 }\)
\(49 = 19 \cdot \sqrt{9} - 8 \)
\(50 = ( 8 + 9 ) \cdot \sqrt{9} - 1 \)
\(51 = 18 \cdot \sqrt{9} - \sqrt{9 }\)
\(52 = ( 8 + 9 ) \cdot \sqrt{9} + 1 \)
\(53 = 8 \cdot 9 - 19 \)
\(54 = \frac{ 18 }{ \sqrt{9} } \cdot 9 \)
\(55 = ( 9 - 1 ) \cdot 8 - 9 \)
\(56 = ( 9 - ( \sqrt{9} - 1 ) ) \cdot 8 \)
\(57 = 18 \cdot \sqrt{9} + \sqrt{9 }\)
\(58 = 8 \cdot \sqrt{9}! + 1 + 9 \)
\(59 = ( 1 + \sqrt{9}! ) \cdot 8 + \sqrt{9 }\)
\(60 = ( 8 - 1 ) \cdot 9 - \sqrt{9 }\)
\(61 = ( 9 - 1 ) \cdot 8 - \sqrt{9 }\)
\(62 = 8 \cdot 9 - 1 - 9 \)
\(63 = \frac{ 189 }{ \sqrt{9 } }\)
\(64 = 8 \cdot 9 + 1 - 9 \)
\(65 = 19 \cdot \sqrt{9} + 8 \)
\(66 = \frac{ 198 }{ \sqrt{9 } }\)
\(67 = 91 - 8 \cdot \sqrt{9 }\)
\(68 = 8 \cdot 9 - 1 - \sqrt{9 }\)
\(69 = 81 - 9 - \sqrt{9 }\)
\(70 = 89 - 19 \)
\(71 = ( 1 + 9 ) \cdot 8 - 9 \)
\(72 = \sqrt{81} \cdot 9 - 9 \)
\(73 = ( 9 - 1 ) \cdot 8 + 9 \)
\(74 = 91 - 8 - 9 \)
\(75 = 81 - 9 + \sqrt{9 }\)
\(76 = 8 \cdot 9 + 1 + \sqrt{9 }\)
\(77 = 91 - 8 - \sqrt{9 }!\)
\(78 = 81 - \frac{ 9 }{ \sqrt{9 } }\)
\(79 = 98 - 19 \)
\(80 = ( 19 - 9 ) \cdot 8 \)
\(81 = 99 - 18 \)
\(82 = \frac{ 9 }{ 9 } + 81 \)
\(83 = 89 \cdot 1 - \sqrt{9 }!\)
\(84 = \frac{ 9 }{ \sqrt{9} } + 81 \)
\(85 = 89 - 1 - \sqrt{9 }\)
\(86 = 89 \cdot 1 - \sqrt{9 }\)
\(87 = 81 - \sqrt{9} + 9 \)
\(88 = 89 - 1^{9 }\)
\(89 = 1^{9} \cdot 89 \)
\(90 = 99 - \sqrt{81 }\)
\(91 = \frac{ 819 }{ 9 }\)
\(92 = 91 - 8 + 9 \)
\(93 = 81 + \sqrt{9} + 9 \)
\(94 = 98 - 1 - \sqrt{9 }\)
\(95 = ( 8 - \sqrt{9} ) \cdot 19 \)
\(96 = 99 - \sqrt{\sqrt{81 }}\)
\(97 = 89 - 1 + 9 \)
\(98 = 89 \cdot 1 + 9 \)
\(99 = \frac{ 891 }{ 9 }\)
\(100 = 1^{8} + 99 \)