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