All 100 targets have a solution.
\(1 = 16^{9 - 9 }\)
\(2 = 9 - ( 16 - 9 )\)
\(3 = \sqrt{16 \cdot 9} - 9 \)
\(4 = \sqrt{169} - 9 \)
\(5 = 96 - 91 \)
\(6 = 9 - ( 9 - 1 \cdot 6 )\)
\(7 = 16 - \sqrt{9 \cdot 9 }\)
\(8 = \sqrt{196} - \sqrt{9 }!\)
\(9 = ( 1^{6} )^{9} \cdot 9 \)
\(10 = \sqrt{169} - \sqrt{9 }\)
\(11 = \sqrt{196} - \sqrt{9 }\)
\(12 = \frac{ 96 }{ 9 - 1 }\)
\(13 = 16 - \frac{ 9 }{ \sqrt{9 } }\)
\(14 = 9 - \sqrt{16} + 9 \)
\(15 = 16 - \frac{ 9 }{ 9 }\)
\(16 = 16 - 9 + 9 \)
\(17 = \frac{ 9 }{ 9 } + 16 \)
\(18 = ( 9 - ( 1 + 6 ) ) \cdot 9 \)
\(19 = \frac{ 9 }{ \sqrt{9} } + 16 \)
\(20 = 9 \cdot 9 - 61 \)
\(21 = ( 16 - 9 ) \cdot \sqrt{9 }\)
\(22 = 91 - 69 \)
\(23 = \sqrt{196} + 9 \)
\(24 = ( \sqrt{169} - 9 )!\)
\(25 = \sqrt{9 \cdot 9} + 16 \)
\(26 = ( 9 - 6 ) \cdot 9 - 1 \)
\(27 = \sqrt{16} \cdot 9 - 9 \)
\(28 = \sqrt{961} - \sqrt{9 }\)
\(29 = \sqrt{9}!! - 691 \)
\(30 = ( 1 + 9 ) \cdot ( 9 - 6 )\)
\(31 = \frac{ 96 }{ \sqrt{9} } - 1 \)
\(32 = \frac{ 96 \cdot 1 }{ \sqrt{9 } }\)
\(33 = \frac{ 96 }{ \sqrt{9} } + 1 \)
\(34 = 16 + 9 + 9 \)
\(35 = 6 \cdot 9 - 19 \)
\(36 = \sqrt{16 \cdot 9 \cdot 9 }\)
\(37 = 91 - 6 \cdot 9 \)
\(38 = 99 - 61 \)
\(39 = \sqrt{169 \cdot 9 }\)
\(40 = \sqrt{961} + 9 \)
\(41 = \sqrt{961 + \sqrt{9 }!!}\)
\(42 = \sqrt{196 \cdot 9 }\)
\(43 = 61 - 9 - 9 \)
\(44 = 6 \cdot 9 - 1 - 9 \)
\(45 = ( 9 - \sqrt{16} ) \cdot 9 \)
\(46 = 6 \cdot 9 + 1 - 9 \)
\(47 = 6 \cdot 9 - 1 - \sqrt{9 }!\)
\(48 = \frac{ 16 \cdot 9 }{ \sqrt{9 } }\)
\(49 = 61 - 9 - \sqrt{9 }\)
\(50 = 69 - 19 \)
\(51 = 19 \cdot \sqrt{9} - 6 \)
\(52 = 61 - \sqrt{9 \cdot 9 }\)
\(53 = 6 \cdot 9 - 1^{9 }\)
\(54 = 1^{9} \cdot 6 \cdot 9 \)
\(55 = 61 - 9 + \sqrt{9 }\)
\(56 = 6 \cdot 9 - 1 + \sqrt{9 }\)
\(57 = ( 9 - 6 ) \cdot 19 \)
\(58 = 61 - \frac{ 9 }{ \sqrt{9 } }\)
\(59 = 69 - 1 - 9 \)
\(60 = ( 19 - 9 ) \cdot 6 \)
\(61 = 61 - 9 + 9 \)
\(62 = \frac{ 9 }{ 9 } + 61 \)
\(63 = ( 16 - 9 ) \cdot 9 \)
\(64 = \frac{ 9 }{ \sqrt{9} } + 61 \)
\(65 = 9 \cdot 9 - 16 \)
\(66 = 69 \cdot 1 - \sqrt{9 }\)
\(67 = 61 - \sqrt{9} + 9 \)
\(68 = 69 - 1^{9 }\)
\(69 = 1^{9} \cdot 69 \)
\(70 = 1^{9} + 69 \)
\(71 = 69 - 1 + \sqrt{9 }\)
\(72 = ( 9 + 9 ) \cdot \sqrt{16 }\)
\(73 = 6 \cdot 9 + 19 \)
\(74 = 9 \cdot 9 - 1 - 6 \)
\(75 = 99 - \sqrt{16 }!\)
\(76 = 91 - 6 - 9 \)
\(77 = 96 - 19 \)
\(78 = 69 \cdot 1 + 9 \)
\(79 = 61 + 9 + 9 \)
\(80 = 9 \cdot 9 - 1^{6 }\)
\(81 = 9^{9 - ( 1 + 6 )}\)
\(82 = 91 - 6 - \sqrt{9 }\)
\(83 = 99 - 16 \)
\(84 = \sqrt{196} \cdot \sqrt{9 }!\)
\(85 = 9 \cdot 9 + \sqrt{16 }\)
\(86 = 96 - 1 - 9 \)
\(87 = 96 \cdot 1 - 9 \)
\(88 = 19 + 69 \)
\(89 = 91 - \frac{ 6 }{ \sqrt{9 } }\)
\(90 = ( 1^{6} + 9 ) \cdot 9 \)
\(91 = 91 - 6 + \sqrt{9 }!\)
\(92 = 99 - 1 - 6 \)
\(93 = \sqrt{961 \cdot 9 }\)
\(94 = 91 - 6 + 9 \)
\(95 = 99 - \sqrt{16 }\)
\(96 = 1^{9} \cdot 96 \)
\(97 = 9 \cdot 9 + 16 \)
\(98 = 99 - 1^{6 }\)
\(99 = 1^{6} \cdot 99 \)
\(100 = 1^{6} + 99 \)