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