All 100 targets have a solution.
\(1 = 9 - ( 16 - 8 )\)
\(2 = \sqrt{6 - \frac{ 18 }{ 9 }}\)
\(3 = \frac{ 9 }{ \frac{ 18 }{ 6 } }\)
\(4 = 6 - \frac{ 18 }{ 9 }\)
\(5 = 91 - 86 \)
\(6 = \sqrt{196} - 8 \)
\(7 = \sqrt{68 - 19 }\)
\(8 = \frac{ 18 }{ 9 } + 6 \)
\(9 = \sqrt{9}^{\frac{ 16 }{ 8 }}\)
\(10 = \frac{ 6! }{ 81 - 9 }\)
\(11 = \frac{ 16 }{ 8 } + 9 \)
\(12 = 81 - 69 \)
\(13 = \frac{ 96 }{ 8 } + 1 \)
\(14 = \frac{ 98 }{ 1 + 6 }\)
\(15 = 96 - 81 \)
\(16 = ( 9 - 8 ) \cdot 16 \)
\(17 = 16 - 8 + 9 \)
\(18 = \frac{ 16 }{ 8 } \cdot 9 \)
\(19 = \sqrt{19^{8 - 6 }}\)
\(20 = \sqrt{16 \cdot 9} + 8 \)
\(21 = \sqrt{169} + 8 \)
\(22 = \sqrt{196} + 8 \)
\(23 = 91 - 68 \)
\(24 = ( 16 - 8 ) \cdot \sqrt{9 }\)
\(25 = \frac{ 81 - 6 }{ \sqrt{9 } }\)
\(26 = \sqrt{\sqrt{16}} \cdot 9 + 8 \)
\(27 = \frac{ 18 }{ 6 } \cdot 9 \)
\(28 = 89 - 61 \)
\(29 = 6 \cdot 8 - 19 \)
\(30 = 16 + 8 + \sqrt{9 }!\)
\(31 = \frac{ 186 }{ \sqrt{9 }! }\)
\(32 = \frac{ 96 }{ \sqrt{\sqrt{81 }} }\)
\(33 = \frac{ 198 }{ 6 }\)
\(34 = \frac{ 68 }{ \sqrt{9} - 1 }\)
\(35 = \sqrt{16} \cdot 8 + \sqrt{9 }\)
\(36 = 6^{\frac{ 18 }{ 9 }}\)
\(37 = 98 - 61 \)
\(38 = ( 8 - 6 ) \cdot 19 \)
\(39 = \sqrt{961} + 8 \)
\(40 = ( 9 - \sqrt{16} ) \cdot 8 \)
\(41 = \sqrt{16} \cdot 8 + 9 \)
\(42 = ( 8 - 1^{9} ) \cdot 6 \)
\(43 = 91 - 6 \cdot 8 \)
\(44 = 61 - 8 - 9 \)
\(45 = \sqrt{81} \cdot 6 - 9 \)
\(46 = 1 \cdot 6 \cdot 9 - 8 \)
\(47 = ( 1 + 6 ) \cdot 8 - 9 \)
\(48 = 18 \cdot \sqrt{9} - 6 \)
\(49 = 68 - 19 \)
\(50 = 61 - 8 - \sqrt{9 }\)
\(51 = 69 - 18 \)
\(52 = ( 1 + 9 ) \cdot 6 - 8 \)
\(53 = ( 6 - 1 ) \cdot 9 + 8 \)
\(54 = ( 18 - 9 ) \cdot 6 \)
\(55 = ( 1 + 6 ) \cdot 9 - 8 \)
\(56 = \frac{ 168 }{ \sqrt{9 } }\)
\(57 = 1 \cdot 6 \cdot 8 + 9 \)
\(58 = 68 - 1 - 9 \)
\(59 = 68 \cdot 1 - 9 \)
\(60 = 69 - \sqrt{81 }\)
\(61 = ( 9 - 8 ) \cdot 61 \)
\(62 = \frac{ 186 }{ \sqrt{9 } }\)
\(63 = \sqrt{81} \cdot 6 + 9 \)
\(64 = ( \frac{ 18 }{ 9 } )^{6 }\)
\(65 = 89 - \sqrt{16 }!\)
\(66 = ( 19 - 8 ) \cdot 6 \)
\(67 = 86 - 19 \)
\(68 = 1^{9} \cdot 68 \)
\(69 = 1^{9} + 68 \)
\(70 = 1^{8} + 69 \)
\(71 = \frac{ 6! }{ 8 } - 19 \)
\(72 = ( 16 - 8 ) \cdot 9 \)
\(73 = 89 - 16 \)
\(74 = 98 - \sqrt{16 }!\)
\(75 = \sqrt{81} \cdot 9 - 6 \)
\(76 = 68 - 1 + 9 \)
\(77 = 68 \cdot 1 + 9 \)
\(78 = 96 - 18 \)
\(79 = 81 - \frac{ 6 }{ \sqrt{9 } }\)
\(80 = ( 8 - \sqrt{9} ) \cdot 16 \)
\(81 = 9^{\frac{ 16 }{ 8 }}\)
\(82 = 98 - 16 \)
\(83 = 89 \cdot 1 - 6 \)
\(84 = 81 - 6 + 9 \)
\(85 = 89 - \sqrt{16 }\)
\(86 = 1^{9} \cdot 86 \)
\(87 = 18 + 69 \)
\(88 = 8 \cdot 9 + 16 \)
\(89 = 1^{6} \cdot 89 \)
\(90 = 1^{6} + 89 \)
\(91 = 98 - 1 - 6 \)
\(92 = 98 \cdot 1 - 6 \)
\(93 = \sqrt{16} + 89 \)
\(94 = 98 - \sqrt{16 }\)
\(95 = 86 \cdot 1 + 9 \)
\(96 = 81 + 6 + 9 \)
\(97 = 1^{8} + 96 \)
\(98 = 1^{6} \cdot 98 \)
\(99 = 819 - 6 !\)
\(100 = \sqrt{\sqrt{16}} + 98 \)