All 100 targets have a solution.
\(1 = 8 - ( 13 - 6 )\)
\(2 = \frac{ 36 }{ 18 }\)
\(3 = \frac{ 18 }{ \sqrt{36 } }\)
\(4 = \frac{ 36 }{ \sqrt{81 } }\)
\(5 = 16 - 3 - 8 \)
\(6 = \frac{ 16 \cdot 3 }{ 8 }\)
\(7 = \frac{ 63 }{ \sqrt{81 } }\)
\(8 = ( \frac{ 16 }{ 8 } )^{3 }\)
\(9 = \sqrt{13 + 68 }\)
\(10 = \frac{ 6 }{ 1 \cdot 3 } + 8 \)
\(11 = \sqrt{361} - 8 \)
\(12 = \sqrt{136 + 8 }\)
\(13 = \frac{ 81 - 3 }{ 6 }\)
\(14 = \frac{ 81 + 3 }{ 6 }\)
\(15 = 13 - 6 + 8 \)
\(16 = 18 - \frac{ 6 }{ 3 }\)
\(17 = \frac{ 136 }{ 8 }\)
\(18 = 36 - 18 \)
\(19 = \frac{ 38 }{ \sqrt{\sqrt{16 }} }\)
\(20 = \frac{ 6 }{ 3 } + 18 \)
\(21 = 16 - 3 + 8 \)
\(22 = 38 - 16 \)
\(23 = \frac{ 138 }{ 6 }\)
\(24 = 18 + \sqrt{36 }\)
\(25 = \frac{ 81 - 6 }{ 3 }\)
\(26 = ( 8 - 6 ) \cdot 13 \)
\(27 = \sqrt{361} + 8 \)
\(28 = \frac{ 168 }{ 3 ! }\)
\(29 = 31 + 6 - 8 \)
\(30 = ( 13 - 8 ) \cdot 6 \)
\(31 = \frac{ 186 }{ 3 ! }\)
\(32 = \frac{ 8^{3} }{ 16 }\)
\(33 = 31 - 6 + 8 \)
\(34 = 38 - \sqrt{16 }\)
\(35 = 6 \cdot 8 - 13 \)
\(36 = \frac{ 18 }{ 3 } \cdot 6 \)
\(37 = 68 - 31 \)
\(38 = 1^{6} \cdot 38 \)
\(39 = 1^{6} + 38 \)
\(40 = 16 \cdot 3 - 8 \)
\(41 = ( 6 + 8 ) \cdot 3 - 1 \)
\(42 = \sqrt{16} + 38 \)
\(43 = 36 - 1 + 8 \)
\(44 = 36 \cdot 1 + 8 \)
\(45 = 63 - 18 \)
\(46 = 6 \cdot 8 + 1 - 3 \)
\(47 = \sqrt{36} \cdot 8 - 1 \)
\(48 = 18 \cdot 3 - 6 \)
\(49 = \sqrt{36} \cdot 8 + 1 \)
\(50 = 61 - 3 - 8 \)
\(51 = \sqrt{81} \cdot 6 - 3 \)
\(52 = 6 \cdot 8 + 1 + 3 \)
\(53 = \frac{ 318 }{ 6 }\)
\(54 = 16 + 38 \)
\(55 = 68 - 13 \)
\(56 = \frac{ 168 }{ 3 }\)
\(57 = \sqrt{81} \cdot 6 + 3 \)
\(58 = 8^{3 - 1} - 6 \)
\(59 = 83 - \sqrt{16 }!\)
\(60 = 18 \cdot 3 + 6 \)
\(61 = 6 \cdot 8 + 13 \)
\(62 = \frac{ 186 }{ 3 }\)
\(63 = 1^{8} \cdot 63 \)
\(64 = 1^{8} + 63 \)
\(65 = 68 \cdot 1 - 3 \)
\(66 = 61 - 3 + 8 \)
\(67 = 83 - 16 \)
\(68 = 1^{3} \cdot 68 \)
\(69 = 1^{3} + 68 \)
\(70 = 13 \cdot 6 - 8 \)
\(71 = 63 \cdot 1 + 8 \)
\(72 = 63 + \sqrt{81 }\)
\(73 = 86 - 13 \)
\(74 = 68 \cdot 1 + 3 !\)
\(75 = 81 - \sqrt{36 }\)
\(76 = 83 - 1 - 6 \)
\(77 = 83 \cdot 1 - 6 \)
\(78 = 81 + 3 - 6 \)
\(79 = 83 - \sqrt{16 }\)
\(80 = ( 8 - 3 ) \cdot 16 \)
\(81 = 13 + 68 \)
\(82 = 83 - 1^{6 }\)
\(83 = \frac{ 6 }{ 3 } + 81 \)
\(84 = 81 - 3 + 6 \)
\(85 = 3 \cdot 8 + 61 \)
\(86 = 13 \cdot 6 + 8 \)
\(87 = \sqrt{16} + 83 \)
\(88 = 83 - 1 + 6 \)
\(89 = 83 \cdot 1 + 6 \)
\(90 = ( 18 - 3 ) \cdot 6 \)
\(91 = 86 - 1 + 3 !\)
\(92 = ( 1 + 3 )! + 68 \)
\(93 = 813 - 6 !\)
\(94 = \frac{ 6! }{ 8 } + 1 + 3 \)
\(95 = ( 3! + 6 ) \cdot 8 - 1 \)
\(96 = 816 - 3 !!\)
\(97 = \sqrt{3^{8}} + 16 \)
\(98 = 13 \cdot 8 - 6 \)
\(99 = 13 + 86 \)
\(100 = \sqrt{\sqrt{( 16 - 3! )^{8 }}}\)