All 100 targets have a solution.
\(1 = 1^{\sqrt{784 }}\)
\(2 = \frac{ 18 - 4 }{ 7 }\)
\(3 = \frac{ 18 }{ ( 7 - 4 )! }\)
\(4 = \frac{ 8 }{ \frac{ 14 }{ 7 } }\)
\(5 = 17 - 4 - 8 \)
\(6 = 8 - \frac{ 14 }{ 7 }\)
\(7 = 81 - 74 \)
\(8 = \sqrt{78 - 14 }\)
\(9 = \sqrt{17 + 8} + 4 \)
\(10 = \frac{ 14 }{ 7 } + 8 \)
\(11 = \frac{ 81 - 4 }{ 7 }\)
\(12 = \frac{ 84 \cdot 1 }{ 7 }\)
\(13 = 84 - 71 \)
\(14 = ( 8 - 7 ) \cdot 14 \)
\(15 = 14 - 7 + 8 \)
\(16 = \frac{ 14 }{ 7 } \cdot 8 \)
\(17 = \sqrt{17^{\frac{ 8 }{ 4 }}}\)
\(18 = ( 17 - 8 ) \cdot \sqrt{4 }\)
\(19 = \frac{ 8 }{ 4 } + 17 \)
\(20 = \sqrt{17 + 8} \cdot 4 \)
\(21 = 17 - 4 + 8 \)
\(22 = \sqrt{841} - 7 \)
\(23 = 71 - 48 \)
\(24 = ( \frac{ 8 }{ \frac{ 14 }{ 7 } } )!\)
\(25 = \sqrt{81 \cdot 4} + 7 \)
\(26 = 41 - 7 - 8 \)
\(27 = \sqrt{784} - 1 \)
\(28 = \sqrt{784} \cdot 1 \)
\(29 = 47 - 18 \)
\(30 = \frac{ \sqrt{17 + 8}! }{ 4 }\)
\(31 = 48 - 17 \)
\(32 = \sqrt{4} \cdot 7 + 18 \)
\(33 = 17 + 4! - 8 \)
\(34 = 81 - 47 \)
\(35 = 18 + 4! - 7 \)
\(36 = \sqrt{841} + 7 \)
\(37 = 78 - 41 \)
\(38 = 47 - \sqrt{81 }\)
\(39 = 47 \cdot 1 - 8 \)
\(40 = 41 + 7 - 8 \)
\(41 = ( 8 - 7 ) \cdot 41 \)
\(42 = ( 14 - 8 ) \cdot 7 \)
\(43 = 18 \cdot \sqrt{4} + 7 \)
\(44 = ( 18 - 7 ) \cdot 4 \)
\(45 = \frac{ \frac{ 7! }{ 14 } }{ 8 }\)
\(46 = 87 - 41 \)
\(47 = 1^{8} \cdot 47 \)
\(48 = 1^{8} + 47 \)
\(49 = 4 \cdot 8 + 17 \)
\(50 = 47 + \sqrt{\sqrt{81 }}\)
\(51 = \frac{ 17 \cdot 4! }{ 8 }\)
\(52 = ( 7 - 1 ) \cdot 8 + 4 \)
\(53 = 81 - 4 \cdot 7 \)
\(54 = ( 7 - 4 ) \cdot 18 \)
\(55 = 47 \cdot 1 + 8 \)
\(56 = 74 - 18 \)
\(57 = 1^{4} + 7 \cdot 8 \)
\(58 = 7^{\sqrt{4}} + \sqrt{81 }\)
\(59 = 71 - 4 - 8 \)
\(60 = 17 \cdot 4 - 8 \)
\(61 = 71 - \sqrt{4} - 8 \)
\(62 = 87 - 1 - 4 !\)
\(63 = \frac{ 18 }{ \sqrt{4} } \cdot 7 \)
\(64 = 78 - 14 \)
\(65 = 17 + 48 \)
\(66 = 74 \cdot 1 - 8 \)
\(67 = 84 - 17 \)
\(68 = ( 8 - 4 ) \cdot 17 \)
\(69 = 71 - \frac{ 8 }{ 4 }\)
\(70 = 7 \cdot 8 + 14 \)
\(71 = 74 - \sqrt{\sqrt{81 }}\)
\(72 = 78 - ( 4 - 1 )!\)
\(73 = 87 - 14 \)
\(74 = 1^{8} \cdot 74 \)
\(75 = 71 - 4 + 8 \)
\(76 = 17 \cdot 4 + 8 \)
\(77 = 78 - 1^{4 }\)
\(78 = 1^{4} \cdot 78 \)
\(79 = 18 \cdot 4 + 7 \)
\(80 = 78 \cdot 1 + \sqrt{4 }\)
\(81 = 74 - 1 + 8 \)
\(82 = 74 \cdot 1 + 8 \)
\(83 = 74 + \sqrt{81 }\)
\(84 = 81 - 4 + 7 \)
\(85 = 1^{7} + 84 \)
\(86 = 87 - 1^{4 }\)
\(87 = 1^{4} \cdot 87 \)
\(88 = 1^{4} + 87 \)
\(89 = \frac{ 178 }{ \sqrt{4 } }\)
\(90 = 14 \cdot 7 - 8 \)
\(91 = 84 \cdot 1 + 7 \)
\(92 = 14 + 78 \)
\(93 = ( 4 - 1 )! + 87 \)
\(94 = \frac{ ( 7 - 1 )! }{ 8 } + 4 \)
\(95 = ( 8 - 4 )! + 71 \)
\(96 = ( 1 + 4 + 7 ) \cdot 8 \)
\(97 = 7 \cdot 8 + 41 \)
\(98 = ( 18 - 4 ) \cdot 7 \)
\(99 = ( 4 + 7 ) \cdot \sqrt{81 }\)
\(100 = ( 17 + 8 ) \cdot 4 \)