All 100 targets have a solution.
\(1 = 14 - 5 - 8 \)
\(2 = \frac{ 18 }{ 4 + 5 }\)
\(3 = \frac{ 54 }{ 18 }\)
\(4 = \frac{ 18 }{ \sqrt{4} } - 5 \)
\(5 = \frac{ 45 }{ \sqrt{81 } }\)
\(6 = \sqrt{54 - 18 }\)
\(7 = 5^{\sqrt{4}} - 18 \)
\(8 = \sqrt{184 - 5 !}\)
\(9 = 18 - 4 - 5 \)
\(10 = \sqrt{81} - 4 + 5 \)
\(11 = 14 + 5 - 8 \)
\(12 = \frac{ 48 }{ 5 - 1 }\)
\(13 = 15 - \frac{ 8 }{ 4 }\)
\(14 = \frac{ 84 }{ 1 + 5 }\)
\(15 = \frac{ 45 }{ \sqrt{\sqrt{81 }} }\)
\(16 = ( \sqrt{81} - 5 ) \cdot 4 \)
\(17 = 58 - 41 \)
\(18 = ( 5 - 4 ) \cdot 18 \)
\(19 = 15 - 4 + 8 \)
\(20 = \frac{ 5! }{ 14 - 8 }\)
\(21 = \frac{ 84 }{ 5 - 1 }\)
\(22 = \sqrt{485 - 1 }\)
\(23 = \sqrt{81 \cdot 4} + 5 \)
\(24 = \sqrt{841} - 5 \)
\(25 = 15 + \sqrt{4} + 8 \)
\(26 = 5 \cdot 8 - 14 \)
\(27 = 45 - 18 \)
\(28 = 148 - 5 !\)
\(29 = \frac{ 5! }{ 8 } + 14 \)
\(30 = ( 14 - 8 ) \cdot 5 \)
\(31 = \sqrt{841 + 5 !}\)
\(32 = ( 5 - 1^{4} ) \cdot 8 \)
\(33 = 48 - 15 \)
\(34 = \sqrt{841} + 5 \)
\(35 = \sqrt{41 + 8} \cdot 5 \)
\(36 = 54 - 18 \)
\(37 = 45 \cdot 1 - 8 \)
\(38 = 4 \cdot 5 + 18 \)
\(39 = 51 - 4 - 8 \)
\(40 = 1^{4} \cdot 5 \cdot 8 \)
\(41 = 18 \cdot \sqrt{4} + 5 \)
\(42 = ( 8 - 5 ) \cdot 14 \)
\(43 = 48 \cdot 1 - 5 \)
\(44 = 58 - 14 \)
\(45 = 54 - \sqrt{81 }\)
\(46 = 1^{8} + 45 \)
\(47 = 4 \cdot 8 + 15 \)
\(48 = 1^{5} \cdot 48 \)
\(49 = 1^{5} + 48 \)
\(50 = \sqrt{4}^{5} + 18 \)
\(51 = 54 - \sqrt{\sqrt{81 }}\)
\(52 = 15 \cdot 4 - 8 \)
\(53 = 45 \cdot 1 + 8 \)
\(54 = 45 + \sqrt{81 }\)
\(55 = 51 - 4 + 8 \)
\(56 = \frac{ 5! }{ 8 } + 41 \)
\(57 = 58 - 1^{4 }\)
\(58 = 1^{4} \cdot 58 \)
\(59 = 1^{4} + 58 \)
\(60 = ( 8 - 4 ) \cdot 15 \)
\(61 = 54 - 1 + 8 \)
\(62 = 14 \cdot 5 - 8 \)
\(63 = 15 + 48 \)
\(64 = 184 - 5 !\)
\(65 = ( \sqrt{81} + 4 ) \cdot 5 \)
\(66 = 18 \cdot 5 - 4 !\)
\(67 = 18 \cdot 4 - 5 \)
\(68 = 15 \cdot 4 + 8 \)
\(69 = 84 - 15 \)
\(70 = ( 18 - 4 ) \cdot 5 \)
\(71 = 85 - 14 \)
\(72 = \sqrt{5184 }\)
\(73 = 5! - ( 48 - 1 )\)
\(74 = 81 - \sqrt{4} - 5 \)
\(75 = ( 8 - 4 )! + 51 \)
\(76 = \sqrt{\sqrt{81}}^{4} - 5 \)
\(77 = 18 \cdot 4 + 5 \)
\(78 = 14 \cdot 5 + 8 \)
\(79 = \frac{ 158 }{ \sqrt{4 } }\)
\(80 = 81 + 4 - 5 \)
\(81 = 5 \cdot 8 + 41 \)
\(82 = 81 - 4 + 5 \)
\(83 = 4 \cdot 8 + 51 \)
\(84 = 1^{5} \cdot 84 \)
\(85 = 1^{5} + 84 \)
\(86 = 18 \cdot 5 - 4 \)
\(87 = 5! - 41 + 8 \)
\(88 = ( 15 - 4 ) \cdot 8 \)
\(89 = 84 \cdot 1 + 5 \)
\(90 = 81 + 4 + 5 \)
\(91 = 5! - \sqrt{841 }\)
\(92 = ( 15 + 8 ) \cdot 4 \)
\(93 = \sqrt{4! + 5!} + 81 \)
\(94 = 18 \cdot 5 + 4 \)
\(95 = \sqrt{1 + 5!} + 84 \)
\(96 = 15 \cdot 8 - 4 !\)
\(97 = 5! - ( 4! - 1^{8 } )\)
\(98 = 5! - 14 - 8 \)
\(99 = 14 + 85 \)
\(100 = ( 18 + \sqrt{4} ) \cdot 5 \)