All 100 targets have a solution.
\(1 = \frac{ 17 - 8 }{ 9 }\)
\(2 = 81 - 79 \)
\(3 = \sqrt{\sqrt{98 - 17 }}\)
\(4 = 91 - 87 \)
\(5 = 7 - \frac{ 18 }{ 9 }\)
\(6 = 9 - \sqrt{17 - 8 }\)
\(7 = \frac{ 71 - 8 }{ 9 }\)
\(8 = \sqrt{( 17 - 9 ) \cdot 8 }\)
\(9 = \sqrt{98 - 17 }\)
\(10 = \frac{ 71 + 9 }{ 8 }\)
\(11 = \sqrt{81} - 7 + 9 \)
\(12 = \frac{ 97 - 1 }{ 8 }\)
\(13 = 91 - 78 \)
\(14 = \sqrt{187 + 9 }\)
\(15 = \frac{ 98 }{ 7 } + 1 \)
\(16 = 97 - 81 \)
\(17 = ( 9 - 8 ) \cdot 17 \)
\(18 = 89 - 71 \)
\(19 = ( 8 - 7 ) \cdot 19 \)
\(20 = 18 - 7 + 9 \)
\(21 = \frac{ 91 }{ 7 } + 8 \)
\(22 = 17 + 8 - \sqrt{9 }\)
\(23 = 7 - 1 + 8 + 9 \)
\(24 = ( 91 - 87 )!\)
\(25 = \frac{ 78 }{ \sqrt{9} } - 1 \)
\(26 = \frac{ 78 \cdot 1 }{ \sqrt{9 } }\)
\(27 = \frac{ 189 }{ 7 }\)
\(28 = \sqrt{781 + \sqrt{9 }}\)
\(29 = \frac{ 87 \cdot 1 }{ \sqrt{9 } }\)
\(30 = \frac{ 87 }{ \sqrt{9} } + 1 \)
\(31 = 17 + 8 + \sqrt{9 }!\)
\(32 = ( 1^{7} + \sqrt{9} ) \cdot 8 \)
\(33 = ( 18 - 7 ) \cdot \sqrt{9 }\)
\(34 = 17 + 8 + 9 \)
\(35 = 91 - 7 \cdot 8 \)
\(36 = ( 9 - 7 ) \cdot 18 \)
\(37 = 7 \cdot 8 - 19 \)
\(38 = \sqrt{\sqrt{9}^{8} - 7!} - 1 \)
\(39 = 7 \cdot \sqrt{9} + 18 \)
\(40 = ( 8 - 1 ) \cdot 7 - 9 \)
\(41 = 8 \cdot \sqrt{9} + 17 \)
\(42 = \frac{ 18 \cdot 7 }{ \sqrt{9 } }\)
\(43 = 17 \cdot \sqrt{9} - 8 \)
\(44 = ( 7 + 8 ) \cdot \sqrt{9} - 1 \)
\(45 = 7 \cdot 9 - 18 \)
\(46 = 7 \cdot 8 - 1 - 9 \)
\(47 = 18 \cdot \sqrt{9} - 7 \)
\(48 = 7 \cdot 8 + 1 - 9 \)
\(49 = 7^{\frac{ 18 }{ 9 }}\)
\(50 = 1 \cdot 7 \cdot 8 - \sqrt{9 }!\)
\(51 = ( 7 - 1 ) \cdot 8 + \sqrt{9 }\)
\(52 = ( 8 - 1 ) \cdot 7 + \sqrt{9 }\)
\(53 = 1 \cdot 7 \cdot 8 - \sqrt{9 }\)
\(54 = 71 - 8 - 9 \)
\(55 = 8 \cdot 9 - 17 \)
\(56 = \frac{ 7! }{ 81 + 9 }\)
\(57 = ( 7 - 1 ) \cdot 8 + 9 \)
\(58 = ( 8 - 1 ) \cdot 7 + 9 \)
\(59 = 78 - 19 \)
\(60 = 71 - 8 - \sqrt{9 }\)
\(61 = 79 - 18 \)
\(62 = ( 7 - 1 ) \cdot 9 + 8 \)
\(63 = ( 18 - 9 ) \cdot 7 \)
\(64 = ( 17 - 9 ) \cdot 8 \)
\(65 = 81 - 7 - 9 \)
\(66 = 71 - 8 + \sqrt{9 }\)
\(67 = ( 1 + 7 ) \cdot 8 + \sqrt{9 }\)
\(68 = 87 - 19 \)
\(69 = 78 \cdot 1 - 9 \)
\(70 = 79 - \sqrt{81 }\)
\(71 = ( 9 - 8 ) \cdot 71 \)
\(72 = 89 - 17 \)
\(73 = 79 - \sqrt{\sqrt{81 }}!\)
\(74 = 78 - 1 - \sqrt{9 }\)
\(75 = 7 \cdot 8 + 19 \)
\(76 = 91 - 7 - 8 \)
\(77 = ( 19 - 8 ) \cdot 7 \)
\(78 = 1^{9} \cdot 78 \)
\(79 = 97 - 18 \)
\(80 = 1^{8} + 79 \)
\(81 = 98 - 17 \)
\(82 = 89 \cdot 1 - 7 \)
\(83 = 81 - 7 + 9 \)
\(84 = 87 \cdot 1 - \sqrt{9 }\)
\(85 = ( 8 - \sqrt{9} ) \cdot 17 \)
\(86 = 78 - 1 + 9 \)
\(87 = 78 \cdot 1 + 9 \)
\(88 = 79 + \sqrt{81 }\)
\(89 = 8 \cdot 9 + 17 \)
\(90 = 1^{7} + 89 \)
\(91 = ( 8 - 7 ) \cdot 91 \)
\(92 = 91 - 7 + 8 \)
\(93 = 87 \cdot 1 + \sqrt{9 }!\)
\(94 = 97 - \sqrt{\sqrt{81 }}\)
\(95 = 87 - 1 + 9 \)
\(96 = ( 19 - 7 ) \cdot 8 \)
\(97 = 18 + 79 \)
\(98 = 1^{8} + 97 \)
\(99 = ( 18 - 7 ) \cdot 9 \)
\(100 = \sqrt{\sqrt{81}} + 97 \)