All 100 targets have a solution.
\(1 = \frac{ 15 - 6 }{ 9 }\)
\(2 = 61 - 59 \)
\(3 = \sqrt{\sqrt{196} - 5 }\)
\(4 = \frac{ 15 + 9 }{ 6 }\)
\(5 = \frac{ 15 }{ 9 - 6 }\)
\(6 = \sqrt{\sqrt{961} + 5 }\)
\(7 = \sqrt{169 - 5 !}\)
\(8 = \sqrt{169} - 5 \)
\(9 = \sqrt{196} - 5 \)
\(10 = \frac{ 15 \cdot 6 }{ 9 }\)
\(11 = 5 \cdot 6 - 19 \)
\(12 = 15 + 6 - 9 \)
\(13 = 15 - \frac{ 6 }{ \sqrt{9 } }\)
\(14 = \frac{ 61 + 9 }{ 5 }\)
\(15 = \sqrt{( 6 + 9 ) \cdot 15 }\)
\(16 = 61 - 5 \cdot 9 \)
\(17 = \sqrt{169 + 5 !}\)
\(18 = 69 - 51 \)
\(19 = \sqrt{196} + 5 \)
\(20 = 16 - 5 + 9 \)
\(21 = ( 9 - 6 )! + 15 \)
\(22 = \frac{ 61 + 5 }{ \sqrt{9 } }\)
\(23 = \frac{ 51 }{ \sqrt{9} } + 6 \)
\(24 = \frac{ 96 }{ 5 - 1 }\)
\(25 = ( 9 - \sqrt{16} ) \cdot 5 \)
\(26 = 91 - 65 \)
\(27 = \sqrt{15 - 6} \cdot 9 \)
\(28 = \frac{ 56 }{ \sqrt{9} - 1 }\)
\(29 = 5 \cdot 9 - 16 \)
\(30 = 15 + 6 + 9 \)
\(31 = \sqrt{16} \cdot 9 - 5 \)
\(32 = ( 5 - \sqrt{9} ) \cdot 16 \)
\(33 = 6 \cdot \sqrt{9} + 15 \)
\(34 = 95 - 61 \)
\(35 = 91 - 56 \)
\(36 = \sqrt{961} + 5 \)
\(37 = 56 - 19 \)
\(38 = 5 \cdot 6 - 1 + 9 \)
\(39 = 6 \cdot 9 - 15 \)
\(40 = ( 9 - 5 )! + 16 \)
\(41 = \sqrt{16} \cdot 9 + 5 \)
\(42 = 51 - 6 - \sqrt{9 }\)
\(43 = 59 - 16 \)
\(44 = ( 1 + 6 ) \cdot 5 + 9 \)
\(45 = 96 - 51 \)
\(46 = 65 - 19 \)
\(47 = 56 \cdot 1 - 9 \)
\(48 = 51 + 6 - 9 \)
\(49 = 169 - 5 !\)
\(50 = 5! - 61 - 9 \)
\(51 = 15 \cdot \sqrt{9} + 6 \)
\(52 = \frac{ 156 }{ \sqrt{9 } }\)
\(53 = 59 \cdot 1 - 6 \)
\(54 = 69 - 15 \)
\(55 = \frac{ 165 }{ \sqrt{9 } }\)
\(56 = 1^{9} \cdot 56 \)
\(57 = 1^{9} + 56 \)
\(58 = 59 - 1^{6 }\)
\(59 = 1^{6} \cdot 59 \)
\(60 = 1^{6} + 59 \)
\(61 = 5 \cdot 9 + 16 \)
\(62 = 65 \cdot 1 - \sqrt{9 }\)
\(63 = \sqrt{16} + 59 \)
\(64 = ( 9 - 5 ) \cdot 16 \)
\(65 = \sqrt{169} \cdot 5 \)
\(66 = 51 + 6 + 9 \)
\(67 = 65 - 1 + \sqrt{9 }\)
\(68 = 69 - 1^{5 }\)
\(69 = 6 \cdot 9 + 15 \)
\(70 = \sqrt{196} \cdot 5 \)
\(71 = 16 \cdot 5 - 9 \)
\(72 = ( 15 - \sqrt{9} ) \cdot 6 \)
\(73 = 65 - 1 + 9 \)
\(74 = 65 \cdot 1 + 9 \)
\(75 = 16 + 59 \)
\(76 = 196 - 5 !\)
\(77 = 16 \cdot 5 - \sqrt{9 }\)
\(78 = ( 5 - 1 + 9 ) \cdot 6 \)
\(79 = 95 - 16 \)
\(80 = 91 - 5 - 6 \)
\(81 = 96 - 15 \)
\(82 = \sqrt{5 - 1} + \frac{ 6! }{ 9 }\)
\(83 = \sqrt{16}! + 59 \)
\(84 = 15 + 69 \)
\(85 = ( 9 - 5 )! + 61 \)
\(86 = \frac{ 516 }{ \sqrt{9 }! }\)
\(87 = 15 \cdot 6 - \sqrt{9 }\)
\(88 = 95 - 1 - 6 \)
\(89 = 16 \cdot 5 + 9 \)
\(90 = 91 + 5 - 6 \)
\(91 = 95 - \sqrt{16 }\)
\(92 = 91 - 5 + 6 \)
\(93 = 95 - \sqrt{\sqrt{16 }}\)
\(94 = 95 - 1^{6 }\)
\(95 = 1^{6} \cdot 95 \)
\(96 = 1^{6} + 95 \)
\(97 = 1^{5} + 96 \)
\(98 = \sqrt{5 - 1} + 96 \)
\(99 = \sqrt{16} + 95 \)
\(100 = 95 - 1 + 6 \)