All 100 targets have a solution.
\(1 = 13 - 4 - 8 \)
\(2 = \frac{ 14 - 8 }{ 3 }\)
\(3 = 41 - 38 \)
\(4 = \sqrt{34 - 18 }\)
\(5 = \sqrt{43 - 18 }\)
\(6 = ( 41 - 38 )!\)
\(7 = 13 + \sqrt{4} - 8 \)
\(8 = \frac{ 18 }{ 3 } + \sqrt{4 }\)
\(9 = 13 + 4 - 8 \)
\(10 = 3 \cdot 8 - 14 \)
\(11 = 13 - \frac{ 8 }{ 4 }\)
\(12 = \frac{ 48 }{ 1 + 3 }\)
\(13 = \sqrt{13^{\frac{ 8 }{ 4 }}}\)
\(14 = \frac{ 18 + 4! }{ 3 }\)
\(15 = \frac{ 8 }{ 4 } + 13 \)
\(16 = 34 - 18 \)
\(17 = 48 - 31 \)
\(18 = ( 14 - 8 ) \cdot 3 \)
\(19 = 4 \cdot 8 - 13 \)
\(20 = ( 13 - 8 ) \cdot 4 \)
\(21 = \frac{ 81 + 3 }{ 4 }\)
\(22 = \sqrt{481 + 3 }\)
\(23 = \frac{ 81 }{ 3 } - 4 \)
\(24 = 38 - 14 \)
\(25 = 43 - 18 \)
\(26 = \sqrt{841} - 3 \)
\(27 = 31 + 4 - 8 \)
\(28 = \frac{ 84 \cdot 1 }{ 3 }\)
\(29 = 31 - \frac{ 8 }{ 4 }\)
\(30 = 3 \cdot 4 + 18 \)
\(31 = \frac{ 81 }{ 3 } + 4 \)
\(32 = \sqrt{841} + 3 \)
\(33 = \frac{ 8 }{ 4 } + 31 \)
\(34 = 43 - \sqrt{81 }\)
\(35 = 48 - 13 \)
\(36 = 41 + 3 - 8 \)
\(37 = 38 - 1^{4 }\)
\(38 = 81 - 43 \)
\(39 = 1^{4} + 38 \)
\(40 = 43 - \sqrt{\sqrt{81 }}\)
\(41 = 34 - 1 + 8 \)
\(42 = 83 - 41 \)
\(43 = 34 + \sqrt{81 }\)
\(44 = 13 \cdot 4 - 8 \)
\(45 = 4 \cdot 8 + 13 \)
\(46 = 4^{3} - 18 \)
\(47 = 81 - 34 \)
\(48 = 1^{3} \cdot 48 \)
\(49 = 1^{3} + 48 \)
\(50 = 14 \cdot 3 + 8 \)
\(51 = 43 \cdot 1 + 8 \)
\(52 = 14 + 38 \)
\(53 = 84 - 31 \)
\(54 = 3 \cdot 4! - 18 \)
\(55 = ( 8 - 4 )! + 31 \)
\(56 = 18 \cdot 3 + \sqrt{4 }\)
\(57 = 81 - 3! \cdot 4 \)
\(58 = 18 \cdot 3 + 4 \)
\(59 = \sqrt{3481 }\)
\(60 = 13 \cdot 4 + 8 \)
\(61 = 13 + 48 \)
\(62 = \frac{ 31 \cdot 8 }{ 4 }\)
\(63 = 3^{4} - 18 \)
\(64 = ( 14 - 3! ) \cdot 8 \)
\(65 = 3 \cdot 8 + 41 \)
\(66 = ( 14 + 8 ) \cdot 3 \)
\(67 = \sqrt{3^{8}} - 14 \)
\(68 = 8^{3 - 1} + 4 \)
\(69 = 83 - 14 \)
\(70 = ( 8 - 3 ) \cdot 14 \)
\(71 = 84 - 13 \)
\(72 = ( 13 - 4 ) \cdot 8 \)
\(73 = 81 - \sqrt{4}^{3 }\)
\(74 = 81 - 3 - 4 \)
\(75 = 18 \cdot 4 + 3 \)
\(76 = 14 \cdot 3! - 8 \)
\(77 = 8^{\sqrt{4}} + 13 \)
\(78 = 83 - 1 - 4 \)
\(79 = 31 + 48 \)
\(80 = 81 + 3 - 4 \)
\(81 = ( 4 - 3 ) \cdot 81 \)
\(82 = 4^{3} + 18 \)
\(83 = 1^{4} \cdot 83 \)
\(84 = ( 13 + 8 ) \cdot 4 \)
\(85 = 1^{3} + 84 \)
\(86 = 83 - 1 + 4 \)
\(87 = \sqrt{841} \cdot 3 \)
\(88 = ( 14 - 3 ) \cdot 8 \)
\(89 = 3! \cdot 8 + 41 \)
\(90 = ( 3 + \sqrt{4} ) \cdot 18 \)
\(91 = 81 + 3! + 4 \)
\(92 = ( 31 - 8 ) \cdot 4 \)
\(93 = 3 \cdot 4 + 81 \)
\(94 = 814 - 3 !!\)
\(95 = \sqrt{3^{8}} + 14 \)
\(96 = ( 3 - 1 ) \cdot 48 \)
\(97 = 13 + 84 \)
\(98 = ( 3! \cdot 8 + 1 ) \cdot \sqrt{4 }\)
\(99 = 3^{4} + 18 \)
\(100 = 13 \cdot 8 - 4 \)