All 100 targets have a solution.
\(1 = 13^{8 - 8 }\)
\(2 = 83 - 81 \)
\(3 = 8 - ( 13 - 8 )\)
\(4 = 18 - 3! - 8 \)
\(5 = 13 - \sqrt{8 \cdot 8 }\)
\(6 = 3 \cdot 8 - 18 \)
\(7 = 18 - 3 - 8 \)
\(8 = ( 1^{3} )^{8} \cdot 8 \)
\(9 = 13 - \sqrt{8 + 8 }\)
\(10 = \frac{ 8 }{ 1 + 3 } + 8 \)
\(11 = \frac{ 18 }{ 3! } + 8 \)
\(12 = 13 - \frac{ 8 }{ 8 }\)
\(13 = 13 - 8 + 8 \)
\(14 = \frac{ 8 }{ 8 } + 13 \)
\(15 = 31 - 8 - 8 \)
\(16 = 18 + 3! - 8 \)
\(17 = \sqrt{8 + 8} + 13 \)
\(18 = 3 - 1 + 8 + 8 \)
\(19 = \frac{ 81 }{ 3 } - 8 \)
\(20 = 38 - 18 \)
\(21 = \sqrt{8 \cdot 8} + 13 \)
\(22 = \frac{ 88 }{ 1 + 3 }\)
\(23 = 18 - 3 + 8 \)
\(24 = \frac{ 18 }{ 3! } \cdot 8 \)
\(25 = 1^{8} + 3 \cdot 8 \)
\(26 = \sqrt{\sqrt{8 + 8}} \cdot 13 \)
\(27 = \sqrt{\frac{ 18^{3} }{ 8 }}\)
\(28 = \sqrt{8 + 8}! + 1 + 3 \)
\(29 = 38 - \sqrt{81 }\)
\(30 = ( 18 - 8 ) \cdot 3 \)
\(31 = 31 - 8 + 8 \)
\(32 = \frac{ 8 }{ 8 } + 31 \)
\(33 = 8 \cdot 8 - 31 \)
\(34 = ( 8 - 1 ) \cdot 3! - 8 \)
\(35 = \frac{ 81 }{ 3 } + 8 \)
\(36 = \sqrt{18 \cdot 8} \cdot 3 \)
\(37 = 38 - 1^{8 }\)
\(38 = 1^{8} \cdot 38 \)
\(39 = 1^{8} + 38 \)
\(40 = ( 13 - 8 ) \cdot 8 \)
\(41 = 38 + \sqrt{\sqrt{81 }}\)
\(42 = 3 \cdot 8 + 18 \)
\(43 = 81 - 38 \)
\(44 = \frac{ 88 }{ 3 - 1 }\)
\(45 = 38 - 1 + 8 \)
\(46 = 18 \cdot 3 - 8 \)
\(47 = 38 + \sqrt{81 }\)
\(48 = \frac{ 18 }{ 3 } \cdot 8 \)
\(49 = ( 8 + 8 ) \cdot 3 + 1 \)
\(50 = ( 8 - 1 ) \cdot 3! + 8 \)
\(51 = 8 \cdot 8 - 13 \)
\(52 = \sqrt{8 + 8} \cdot 13 \)
\(53 = ( 8 - 1 ) \cdot 8 - 3 \)
\(54 = ( 1^{8} + 8 ) \cdot 3 !\)
\(55 = \sqrt{8 + 8}! + 31 \)
\(56 = 18 + 38 \)
\(57 = 88 - 31 \)
\(58 = 1 \cdot 8 \cdot 8 - 3 !\)
\(59 = ( 8 - 1 ) \cdot 8 + 3 \)
\(60 = ( 18 - 8 ) \cdot 3 !\)
\(61 = 1 \cdot 8 \cdot 8 - 3 \)
\(62 = 18 \cdot 3 + 8 \)
\(63 = \sqrt{3^{8}} - 18 \)
\(64 = 88 - ( 1 + 3 )!\)
\(65 = 83 - 18 \)
\(66 = 3! \cdot 8 + 18 \)
\(67 = 81 - 3! - 8 \)
\(68 = 8 \cdot 8 + 1 + 3 \)
\(69 = \sqrt{81} \cdot 8 - 3 \)
\(70 = 81 - 3 - 8 \)
\(71 = 8 \cdot 8 + 1 + 3 !\)
\(72 = ( 1^{3} + 8 ) \cdot 8 \)
\(73 = \sqrt{( 1 \cdot 3 )^{8}} - 8 \)
\(74 = 83 - \sqrt{81 }\)
\(75 = 88 - 13 \)
\(76 = 81 + 3 - 8 \)
\(77 = 8 \cdot 8 + 13 \)
\(78 = ( 18 + 8 ) \cdot 3 \)
\(79 = 81 + 3! - 8 \)
\(80 = 83 - \sqrt{\sqrt{81 }}\)
\(81 = \frac{ 3^{8} }{ 81 }\)
\(82 = 83 - 1^{8 }\)
\(83 = 1^{8} \cdot 83 \)
\(84 = 1^{8} + 83 \)
\(85 = 88 \cdot 1 - 3 \)
\(86 = 81 - 3 + 8 \)
\(87 = 88 - 1^{3 }\)
\(88 = 1^{3} \cdot 88 \)
\(89 = 1^{3} + 88 \)
\(90 = ( 8 - 3 ) \cdot 18 \)
\(91 = 83 \cdot 1 + 8 \)
\(92 = \sqrt{81} + 83 \)
\(93 = 88 - 1 + 3 !\)
\(94 = 88 \cdot 1 + 3 !\)
\(95 = 8 \cdot 8 + 31 \)
\(96 = 13 \cdot 8 - 8 \)
\(97 = ( 8 + 8 ) \cdot 3! + 1 \)
\(98 = 818 - 3 !!\)
\(99 = \sqrt{3^{8}} + 18 \)
\(100 = 18 \cdot 3! - 8 \)