All 100 targets have a solution.
\(1 = 18^{3 - 3 }\)
\(2 = 13 - 3 - 8 \)
\(3 = \frac{ 18 }{ 3 } - 3 \)
\(4 = \frac{ 33 - 1 }{ 8 }\)
\(5 = \sqrt{38 - 13 }\)
\(6 = \frac{ 18 }{ 3! } + 3 \)
\(7 = 38 - 31 \)
\(8 = 13 + 3 - 8 \)
\(9 = \frac{ 18 }{ 3 } + 3 \)
\(10 = \frac{ 3 }{ 3 } + \sqrt{81 }\)
\(11 = 3 \cdot 8 - 13 \)
\(12 = 18 - 3 - 3 \)
\(13 = \frac{ 31 + 8 }{ 3 }\)
\(14 = 38 - ( 1 + 3 )!\)
\(15 = 33 - 18 \)
\(16 = 18 - \frac{ 3! }{ 3 }\)
\(17 = 18 - \frac{ 3 }{ 3 }\)
\(18 = 13 - 3 + 8 \)
\(19 = \frac{ 3 }{ 3 } + 18 \)
\(20 = 31 - 3 - 8 \)
\(21 = 18 - 3 + 3 !\)
\(22 = 3 \cdot 8 + 1 - 3 \)
\(23 = \frac{ 138 }{ 3 ! }\)
\(24 = 33 - \sqrt{81 }\)
\(25 = 38 - 13 \)
\(26 = 31 + 3 - 8 \)
\(27 = 3 \cdot 3 + 18 \)
\(28 = \frac{ 81 + 3 }{ 3 }\)
\(29 = 31 + 3! - 8 \)
\(30 = \frac{ 81 }{ 3 } + 3 \)
\(31 = 13 \cdot 3 - 8 \)
\(32 = 33 - 1^{8 }\)
\(33 = 1^{8} \cdot 33 \)
\(34 = 1^{8} + 33 \)
\(35 = 38 \cdot 1 - 3 \)
\(36 = 31 - 3 + 8 \)
\(37 = 3 \cdot 8 + 13 \)
\(38 = 1^{3} \cdot 38 \)
\(39 = 1^{3} + 38 \)
\(40 = 33 - 1 + 8 \)
\(41 = 33 \cdot 1 + 8 \)
\(42 = 33 + \sqrt{81 }\)
\(43 = 38 - 1 + 3 !\)
\(44 = 38 \cdot 1 + 3 !\)
\(45 = ( 18 - 3 ) \cdot 3 \)
\(46 = \frac{ 138 }{ 3 }\)
\(47 = 13 \cdot 3 + 8 \)
\(48 = 81 - 33 \)
\(49 = ( 3 + 3 ) \cdot 8 + 1 \)
\(50 = \sqrt{3^{8}} - 31 \)
\(51 = 13 + 38 \)
\(52 = 83 - 31 \)
\(53 = \frac{ 318 }{ 3 ! }\)
\(54 = 81 - 3^{3 }\)
\(55 = 3 \cdot 8 + 31 \)
\(56 = ( 13 - 3! ) \cdot 8 \)
\(57 = 18 \cdot 3 + 3 \)
\(58 = 8^{3 - 1} - 3 !\)
\(59 = 83 - ( 1 + 3 )!\)
\(60 = 18 \cdot 3 + 3 !\)
\(61 = \frac{ 183 }{ 3 }\)
\(62 = ( 8 - 3! ) \cdot 31 \)
\(63 = ( 13 + 8 ) \cdot 3 \)
\(64 = 8^{3 - 1^{3 }}\)
\(65 = ( 8 - 3 ) \cdot 13 \)
\(66 = ( 1 \cdot 3 + 8 ) \cdot 3 !\)
\(67 = 8^{3 - 1} + 3 \)
\(68 = \sqrt{3^{8}} - 13 \)
\(69 = 31 + 38 \)
\(70 = 83 - 13 \)
\(71 = 3 \cdot 3 \cdot 8 - 1 \)
\(72 = 81 - 3 \cdot 3 \)
\(73 = 3^{1 + 3} - 8 \)
\(74 = \sqrt{3^{8}} - 1 - 3 !\)
\(75 = 81 - 3 - 3 \)
\(76 = ( 3 - 1 ) \cdot 38 \)
\(77 = 83 \cdot 1 - 3 !\)
\(78 = 81 - 3! + 3 \)
\(79 = 83 - 1 - 3 \)
\(80 = ( 13 - 3 ) \cdot 8 \)
\(81 = \frac{ 81 }{ 3 } \cdot 3 \)
\(82 = \frac{ 3 }{ 3 } + 81 \)
\(83 = 1^{3} \cdot 83 \)
\(84 = 1^{3} + 83 \)
\(85 = 31 \cdot 3 - 8 \)
\(86 = 83 \cdot 1 + 3 \)
\(87 = 81 + 3 + 3 \)
\(88 = 83 - 1 + 3 !\)
\(89 = ( 8 - 3 )! - 31 \)
\(90 = 3 \cdot 3 + 81 \)
\(91 = \frac{ 3^{3!} - 1 }{ 8 }\)
\(92 = \frac{ 3!! }{ 8 } - 1 + 3 \)
\(93 = 813 - 3 !!\)
\(94 = \sqrt{3^{8}} + 13 \)
\(95 = ( 3! + 3! ) \cdot 8 - 1 \)
\(96 = 13 + 83 \)
\(97 = ( 3! + 3! ) \cdot 8 + 1 \)
\(98 = 13 \cdot 8 - 3 !\)
\(99 = 33 \cdot \sqrt{\sqrt{81 }}\)
\(100 = \sqrt{\sqrt{( 13 - 3 )^{8 }}}\)