All 100 targets have a solution.
\(1 = 97 - 96 \)
\(2 = 7 - ( 6 - \frac{ 9 }{ 9 } )\)
\(3 = \frac{ 9 }{ \frac{ 6 }{ 9 - 7 } }\)
\(4 = \frac{ 6^{9 - 7} }{ 9 }\)
\(5 = 9 \cdot 9 - 76 \)
\(6 = 69 - 7 \cdot 9 \)
\(7 = \sqrt{67 - 9 - 9 }\)
\(8 = \sqrt{79 - 6 - 9 }\)
\(9 = 6! - 79 \cdot 9 \)
\(10 = 79 - 69 \)
\(11 = \sqrt{9} - ( 7 - 6 ) + 9 \)
\(12 = \frac{ 6 }{ 9 - 7 } + 9 \)
\(13 = 6 + 7 - 9 + 9 \)
\(14 = 9 \cdot 9 - 67 \)
\(15 = \frac{ 96 + 9 }{ 7 }\)
\(16 = \frac{ 69 }{ \sqrt{9} } - 7 \)
\(17 = 96 - 79 \)
\(18 = ( 7 - 6 ) \cdot 9 + 9 \)
\(19 = 7 - 6 + 9 + 9 \)
\(20 = ( 9 - 6 ) \cdot 9 - 7 \)
\(21 = ( 9 - 7 ) \cdot 6 + 9 \)
\(22 = 76 - \sqrt{9}! \cdot 9 \)
\(23 = 99 - 76 \)
\(24 = \frac{ 96 }{ 7 - \sqrt{9 } }\)
\(25 = 79 - 6 \cdot 9 \)
\(26 = \sqrt{679 - \sqrt{9 }}\)
\(27 = 6! - 99 \cdot 7 \)
\(28 = 97 - 69 \)
\(29 = ( 9 - \sqrt{9} ) \cdot 6 - 7 \)
\(30 = \frac{ 69 }{ \sqrt{9} } + 7 \)
\(31 = \sqrt{967 - \sqrt{9 }!}\)
\(32 = 99 - 67 \)
\(33 = 96 - 7 \cdot 9 \)
\(34 = ( 9 - 6 ) \cdot 9 + 7 \)
\(35 = ( 6 - \frac{ 9 }{ 9 } ) \cdot 7 \)
\(36 = ( 6 + 7 - 9 ) \cdot 9 \)
\(37 = \sqrt{\sqrt{9}^{6}} + 7 + \sqrt{9 }\)
\(38 = 6 \cdot 9 - 7 - 9 \)
\(39 = \frac{ 96 }{ \sqrt{9} } + 7 \)
\(40 = 67 - \sqrt{9} \cdot 9 \)
\(41 = \sqrt{9}!! - 679 \)
\(42 = 6 \cdot 7 - 9 + 9 \)
\(43 = 97 - 6 \cdot 9 \)
\(44 = 6 \cdot 9 - 7 - \sqrt{9 }\)
\(45 = 6^{9 - 7} + 9 \)
\(46 = 7^{\frac{ 6 }{ \sqrt{9} }} - \sqrt{9 }\)
\(47 = \frac{ 6! }{ 9 + 9 } + 7 \)
\(48 = \frac{ 96 }{ 9 - 7 }\)
\(49 = 67 - 9 - 9 \)
\(50 = 6 \cdot 9 - 7 + \sqrt{9 }\)
\(51 = ( 9 - 6 )! \cdot 7 + 9 \)
\(52 = 6 \cdot 9 + 7 - 9 \)
\(53 = 69 - 7 - 9 \)
\(54 = 96 - 7 \cdot \sqrt{9 }!\)
\(55 = 67 - 9 - \sqrt{9 }\)
\(56 = 6 \cdot 9 - 7 + 9 \)
\(57 = 99 - 6 \cdot 7 \)
\(58 = 76 - 9 - 9 \)
\(59 = 69 - 7 - \sqrt{9 }\)
\(60 = 6 \cdot 7 + 9 + 9 \)
\(61 = 67 - 9 + \sqrt{9 }\)
\(62 = 7 \cdot 9 - \frac{ 6 }{ \sqrt{9 }! }\)
\(63 = ( 9 - 6 ) \cdot 7 \cdot \sqrt{9 }\)
\(64 = 79 - 6 - 9 \)
\(65 = 69 - 7 + \sqrt{9 }\)
\(66 = 67 - \frac{ 9 }{ 9 }\)
\(67 = 67 - 9 + 9 \)
\(68 = \frac{ 9 }{ 9 } + 67 \)
\(69 = \sqrt{69^{9 - 7 }}\)
\(70 = \frac{ 9 }{ \sqrt{9} } + 67 \)
\(71 = 69 - 7 + 9 \)
\(72 = ( 9 - ( 7 - 6 ) ) \cdot 9 \)
\(73 = 67 - \sqrt{9} + 9 \)
\(74 = 9^{\frac{ 6 }{ \sqrt{9} }} - 7 \)
\(75 = 76 - \frac{ 9 }{ 9 }\)
\(76 = 76 - 9 + 9 \)
\(77 = \frac{ 9 }{ 9 } + 76 \)
\(78 = 7 \cdot 9 + 6 + 9 \)
\(79 = 799 - 6 !\)
\(80 = 96 - 7 - 9 \)
\(81 = \frac{ 6 }{ \sqrt{9} } + 79 \)
\(82 = 79 - 6 + 9 \)
\(83 = 96 - 7 - \sqrt{9 }!\)
\(84 = \frac{ 7! }{ 69 - 9 }\)
\(85 = 67 + 9 + 9 \)
\(86 = 99 - 6 - 7 \)
\(87 = ( 7 + 9 ) \cdot 6 - 9 \)
\(88 = 76 + \sqrt{9} + 9 \)
\(89 = 96 - \frac{ 7! }{ \sqrt{9 }!! }\)
\(90 = 7 \cdot \sqrt{9} + 69 \)
\(91 = 97 - ( 9 - 6 )!\)
\(92 = 96 - 7 + \sqrt{9 }\)
\(93 = ( 7 - \sqrt{9} )! + 69 \)
\(94 = 76 + 9 + 9 \)
\(95 = 97 - \frac{ 6 }{ \sqrt{9 } }\)
\(96 = \sqrt{96^{9 - 7 }}\)
\(97 = 6 \cdot \sqrt{9} + 79 \)
\(98 = 96 - 7 + 9 \)
\(99 = ( 7 - 6 ) \cdot 99 \)
\(100 = 97 - 6 + 9 \)