All 100 targets have a solution.
\(1 = ( 8 - 7 )^{24 }\)
\(2 = 8 - \frac{ 42 }{ 7 }\)
\(3 = \sqrt{24 - 7 - 8 }\)
\(4 = 7 - \frac{ 24 }{ 8 }\)
\(5 = 4 \cdot 8 - 27 \)
\(6 = \sqrt{78 - 42 }\)
\(7 = \sqrt{\frac{ 28 }{ 4 } \cdot 7 }\)
\(8 = 82 - 74 \)
\(9 = 24 - 7 - 8 \)
\(10 = \frac{ 24 }{ 8 } + 7 \)
\(11 = \sqrt{24 - 8} + 7 \)
\(12 = 84 - 72 \)
\(13 = \frac{ 72 }{ 8 } + 4 \)
\(14 = \frac{ \sqrt{784} }{ 2 }\)
\(15 = 27 - 4 - 8 \)
\(16 = \frac{ 28 \cdot 4 }{ 7 }\)
\(17 = 28 - 4 - 7 \)
\(18 = \frac{ 72 }{ 8 - 4 }\)
\(19 = 47 - 28 \)
\(20 = \frac{ 72 + 8 }{ 4 }\)
\(21 = 48 - 27 \)
\(22 = 28 - ( 7 - 4 )!\)
\(23 = 24 + 7 - 8 \)
\(24 = 72 - 48 \)
\(25 = 24 - 7 + 8 \)
\(26 = \sqrt{784} - 2 \)
\(27 = 42 - 7 - 8 \)
\(28 = \sqrt{782 + \sqrt{4 }}\)
\(29 = \frac{ 8 }{ 4 } + 27 \)
\(30 = \sqrt{784} + 2 \)
\(31 = 27 - 4 + 8 \)
\(32 = 7 \cdot 8 - 24 \)
\(33 = \frac{ 74 - 8 }{ 2 }\)
\(34 = 48 - 2 \cdot 7 \)
\(35 = 82 - 47 \)
\(36 = 78 - 42 \)
\(37 = 47 - 2 - 8 \)
\(38 = ( 27 - 8 ) \cdot \sqrt{4 }\)
\(39 = 24 + 7 + 8 \)
\(40 = 72 - 4 \cdot 8 \)
\(41 = 42 + 7 - 8 \)
\(42 = ( 8 - 7 ) \cdot 42 \)
\(43 = 42 - 7 + 8 \)
\(44 = 2^{7} - 84 \)
\(45 = 87 - 42 \)
\(46 = 74 - 28 \)
\(47 = ( 2 + 8 ) \cdot 4 + 7 \)
\(48 = \frac{ 42 }{ 7 } \cdot 8 \)
\(49 = \frac{ 28 }{ 4 } \cdot 7 \)
\(50 = 74 - ( \frac{ 8 }{ 2 } )!\)
\(51 = \frac{ 8 }{ 2 } + 47 \)
\(52 = 78 - 2 - 4 !\)
\(53 = 47 - 2 + 8 \)
\(54 = 78 - 24 \)
\(55 = \sqrt{47^{2}} + 8 \)
\(56 = \sqrt{784} \cdot 2 \)
\(57 = 84 - 27 \)
\(58 = 74 - 2 \cdot 8 \)
\(59 = \frac{ 472 }{ 8 }\)
\(60 = 72 - 4 - 8 \)
\(61 = 87 - 2 - 4 !\)
\(62 = 2 \cdot 7 + 48 \)
\(63 = 87 - 24 \)
\(64 = 74 - 2 - 8 \)
\(65 = 82 - 4! + 7 \)
\(66 = 72 + \sqrt{4} - 8 \)
\(67 = 8^{2} - 4 + 7 \)
\(68 = 72 + 4 - 8 \)
\(69 = 72 - \frac{ 4! }{ 8 }\)
\(70 = 72 - \frac{ 8 }{ 4 }\)
\(71 = 82 - 4 - 7 \)
\(72 = 78 - 2 - 4 \)
\(73 = 82 - \sqrt{4} - 7 \)
\(74 = \frac{ 8 }{ 4 } + 72 \)
\(75 = 27 + 48 \)
\(76 = ( 27 - 8 ) \cdot 4 \)
\(77 = 7^{\sqrt{4}} + 28 \)
\(78 = ( 47 - 8 ) \cdot 2 \)
\(79 = 82 + 4 - 7 \)
\(80 = 7 \cdot 8 + 24 \)
\(81 = 87 - 2 - 4 \)
\(82 = ( 48 - 7 ) \cdot 2 \)
\(83 = 87 - 2 - \sqrt{4 }\)
\(84 = ( 28 - 7 ) \cdot 4 \)
\(85 = 82 - 4 + 7 \)
\(86 = 47 \cdot 2 - 8 \)
\(87 = 82 - \sqrt{4} + 7 \)
\(88 = 72 + 4! - 8 \)
\(89 = 48 \cdot 2 - 7 \)
\(90 = 2 \cdot 8 + 74 \)
\(91 = 8^{\sqrt{4}} + 27 \)
\(92 = ( 2 \cdot 8 + 7 ) \cdot 4 \)
\(93 = 82 + 4 + 7 \)
\(94 = 2^{4} + 78 \)
\(95 = 2 \cdot 4 + 87 \)
\(96 = \frac{ 28 \cdot 4! }{ 7 }\)
\(97 = 7^{2} + 48 \)
\(98 = 7 \cdot 8 + 42 \)
\(99 = 82 + 4! - 7 \)
\(100 = 27 \cdot 4 - 8 \)