All 100 targets have a solution.
\(1 = 15 - 6 - 8 \)
\(2 = 5 - \frac{ 18 }{ 6 }\)
\(3 = 61 - 58 \)
\(4 = \sqrt{81 - 65 }\)
\(5 = \sqrt{81 - 56 }\)
\(6 = ( 61 - 58 )!\)
\(7 = \frac{ 16 }{ 8 } + 5 \)
\(8 = \frac{ 18 }{ 6 } + 5 \)
\(9 = \sqrt{85 - \sqrt{16 }}\)
\(10 = \frac{ 16 \cdot 5 }{ 8 }\)
\(11 = \sqrt{15 - 6} + 8 \)
\(12 = 5 \cdot 6 - 18 \)
\(13 = 15 + 6 - 8 \)
\(14 = \frac{ 85 - 1 }{ 6 }\)
\(15 = \frac{ 18 \cdot 5 }{ 6 }\)
\(16 = 81 - 65 \)
\(17 = 68 - 51 \)
\(18 = ( 6 - 5 ) \cdot 18 \)
\(19 = 16 - 5 + 8 \)
\(20 = \frac{ 15 \cdot 8 }{ 6 }\)
\(21 = 61 - 5 \cdot 8 \)
\(22 = ( 8 - 5 )! + 16 \)
\(23 = \frac{ 18 + 5! }{ 6 }\)
\(24 = 85 - 61 \)
\(25 = 81 - 56 \)
\(26 = \sqrt{681 - 5 }\)
\(27 = \sqrt{16} \cdot 8 - 5 \)
\(28 = \sqrt{16} \cdot 5 + 8 \)
\(29 = 15 + 6 + 8 \)
\(30 = ( 8 - 6 ) \cdot 15 \)
\(31 = \frac{ 5! }{ 8 } + 16 \)
\(32 = ( \frac{ 16 }{ 8 } )^{5 }\)
\(33 = 6 \cdot 8 - 15 \)
\(34 = 58 - \sqrt{16 }!\)
\(35 = 86 - 51 \)
\(36 = 5 \cdot 8 - \sqrt{16 }\)
\(37 = 51 - 6 - 8 \)
\(38 = 56 - 18 \)
\(39 = \frac{ 6! }{ 8 } - 51 \)
\(40 = ( 16 - 8 ) \cdot 5 \)
\(41 = ( 8 - 1 ) \cdot 5 + 6 \)
\(42 = 58 - 16 \)
\(43 = \frac{ 86 }{ \sqrt{5 - 1 } }\)
\(44 = 5 \cdot 8 + \sqrt{16 }\)
\(45 = \frac{ 6! }{ 18 } + 5 \)
\(46 = 61 - \frac{ 5! }{ 8 }\)
\(47 = 65 - 18 \)
\(48 = 168 - 5 !\)
\(49 = 51 + 6 - 8 \)
\(50 = 56 - \sqrt{\sqrt{81 }}!\)
\(51 = 58 - 1 - 6 \)
\(52 = 58 \cdot 1 - 6 \)
\(53 = 68 - 15 \)
\(54 = 58 - \sqrt{16 }\)
\(55 = 56 - 1^{8 }\)
\(56 = 65 - \sqrt{81 }\)
\(57 = 1^{8} + 56 \)
\(58 = 1^{6} \cdot 58 \)
\(59 = 1^{6} + 58 \)
\(60 = ( 18 - 6 ) \cdot 5 \)
\(61 = 85 - \sqrt{16 }!\)
\(62 = \sqrt{16} + 58 \)
\(63 = 6 \cdot 8 + 15 \)
\(64 = 56 \cdot 1 + 8 \)
\(65 = 56 + \sqrt{81 }\)
\(66 = 186 - 5 !\)
\(67 = 68 - 1^{5 }\)
\(68 = \frac{ 51 \cdot 8 }{ 6 }\)
\(69 = 85 - 16 \)
\(70 = 81 - 5 - 6 \)
\(71 = 86 - 15 \)
\(72 = ( 15 - 6 ) \cdot 8 \)
\(73 = 65 \cdot 1 + 8 \)
\(74 = 16 + 58 \)
\(75 = \frac{ 6! }{ 8 } - 15 \)
\(76 = \frac{ 5! }{ 8 } + 61 \)
\(77 = ( 5 + 8 ) \cdot 6 - 1 \)
\(78 = ( 18 - 5 ) \cdot 6 \)
\(79 = 85 \cdot 1 - 6 \)
\(80 = 81 + 5 - 6 \)
\(81 = 85 - \sqrt{16 }\)
\(82 = 15 \cdot 6 - 8 \)
\(83 = 15 + 68 \)
\(84 = 18 \cdot 5 - 6 \)
\(85 = 1^{6} \cdot 85 \)
\(86 = 1^{6} + 85 \)
\(87 = 1^{5} + 86 \)
\(88 = ( 16 - 5 ) \cdot 8 \)
\(89 = \sqrt{16} + 85 \)
\(90 = 85 - 1 + 6 \)
\(91 = 85 \cdot 1 + 6 \)
\(92 = 81 + 5 + 6 \)
\(93 = \sqrt{\frac{ 6! }{ 5 }} + 81 \)
\(94 = \frac{ 6! }{ 8 } - 1 + 5 \)
\(95 = 815 - 6 !\)
\(96 = 18 \cdot 5 + 6 \)
\(97 = \sqrt{1 + 5!} + 86 \)
\(98 = 15 \cdot 6 + 8 \)
\(99 = 6 \cdot 8 + 51 \)
\(100 = \sqrt{\sqrt{5^{8}} \cdot 16 }\)