All 100 targets have a solution.
\(1 = \frac{ 56 }{ 8 } - 6 \)
\(2 = \sqrt{56 + 8} - 6 \)
\(3 = 68 - 65 \)
\(4 = \frac{ 56 }{ 6 + 8 }\)
\(5 = 6 - ( 6 - 5 )^{8 }\)
\(6 = ( 68 - 65 )!\)
\(7 = \sqrt{85 - 6 \cdot 6 }\)
\(8 = 66 - 58 \)
\(9 = ( 6 - 5 )^{6} + 8 \)
\(10 = \sqrt{5 - \frac{ 6 }{ 6 }} + 8 \)
\(11 = \frac{ 66 }{ ( 8 - 5 )! }\)
\(12 = 68 - 56 \)
\(13 = \frac{ 56 }{ 8 } + 6 \)
\(14 = \sqrt{56 + 8} + 6 \)
\(15 = \frac{ 6! }{ 56 - 8 }\)
\(16 = \frac{ 86 - 6 }{ 5 }\)
\(17 = 65 - 6 \cdot 8 \)
\(18 = ( 5 + 6 - 8 ) \cdot 6 \)
\(19 = 85 - 66 \)
\(20 = \sqrt{( 56 - 6 ) \cdot 8 }\)
\(21 = 86 - 65 \)
\(22 = 58 - 6 \cdot 6 \)
\(23 = 6 \cdot 6 - 5 - 8 \)
\(24 = ( \frac{ 56 }{ 6 + 8 } )!\)
\(25 = \frac{ 6! }{ 8 } - 65 \)
\(26 = 66 - 5 \cdot 8 \)
\(27 = \frac{ 5! - 6 }{ 6 } + 8 \)
\(28 = \frac{ 56 }{ 8 - 6 }\)
\(29 = 65 - \sqrt{\sqrt{6^{8 }}}\)
\(30 = 86 - 56 \)
\(31 = 5^{8 - 6} + 6 \)
\(32 = ( 5 - \frac{ 6 }{ 6 } ) \cdot 8 \)
\(33 = 6 \cdot 6 + 5 - 8 \)
\(34 = \frac{ 6! }{ 8 } - 56 \)
\(35 = 6! - 685 \)
\(36 = 6^{\frac{ 6 }{ 8 - 5 }}\)
\(37 = 6 \cdot 8 - 5 - 6 \)
\(38 = 68 - 5 \cdot 6 \)
\(39 = \sqrt{5^{6}} - 86 \)
\(40 = 5! - 86 + 6 \)
\(41 = 6^{8 - 6} + 5 \)
\(42 = 56 - 6 - 8 \)
\(43 = \sqrt{6 \cdot 6} \cdot 8 - 5 \)
\(44 = 5 \cdot 6 + 6 + 8 \)
\(45 = ( \frac{ 6 }{ 6 } + 8 ) \cdot 5 \)
\(46 = 58 - 6 - 6 \)
\(47 = 6 \cdot 8 + 5 - 6 \)
\(48 = \sqrt{56 + 8} \cdot 6 \)
\(49 = 85 - 6 \cdot 6 \)
\(50 = \sqrt{\sqrt{\sqrt{( 56 - 6 )^{8 }}}}\)
\(51 = 65 - 6 - 8 \)
\(52 = 58 - \sqrt{6 \cdot 6 }\)
\(53 = 66 - 5 - 8 \)
\(54 = 56 + 6 - 8 \)
\(55 = \frac{ 8! }{ 6! } + 5 - 6 \)
\(56 = 86 - 5 \cdot 6 \)
\(57 = 58 - \frac{ 6 }{ 6 }\)
\(58 = 56 - 6 + 8 \)
\(59 = \frac{ 6 }{ 6 } + 58 \)
\(60 = 66 - ( 8 - 5 )!\)
\(61 = \sqrt{\sqrt{\sqrt{( 66 - 5 )^{8 }}}}\)
\(62 = 6! - 658 \)
\(63 = 65 + 6 - 8 \)
\(64 = \sqrt{6 \cdot 6} + 58 \)
\(65 = \sqrt{65^{8 - 6 }}\)
\(66 = 86 - \frac{ 5! }{ 6 }\)
\(67 = 65 - 6 + 8 \)
\(68 = ( 6 - 5 ) \cdot 68 \)
\(69 = 66 - 5 + 8 \)
\(70 = 56 + 6 + 8 \)
\(71 = \sqrt{\sqrt{\sqrt{( 65 + 6 )^{8 }}}}\)
\(72 = ( 8 - 5 )! + 66 \)
\(73 = 85 - 6 - 6 \)
\(74 = ( 5 + 6 ) \cdot 6 + 8 \)
\(75 = 86 - 5 - 6 \)
\(76 = \frac{ 6! }{ 5 } - 68 \)
\(77 = \sqrt{5^{6}} - 6 \cdot 8 \)
\(78 = 5 \cdot 6 + 6 \cdot 8 \)
\(79 = 65 + 6 + 8 \)
\(80 = \sqrt{\frac{ 6! }{ 5 }} + 68 \)
\(81 = \frac{ 5! }{ 8 } + 66 \)
\(82 = \frac{ 656 }{ 8 }\)
\(83 = \frac{ 6! - 56 }{ 8 }\)
\(84 = 85 - \frac{ 6 }{ 6 }\)
\(85 = 85 - 6 + 6 \)
\(86 = \frac{ 6 }{ 6 } + 85 \)
\(87 = 86 - 5 + 6 \)
\(88 = \frac{ 5! }{ 6 } + 68 \)
\(89 = ( 6 + 8 ) \cdot 6 + 5 \)
\(90 = \frac{ 6! }{ \sqrt{56 + 8 } }\)
\(91 = \sqrt{6 \cdot 6} + 85 \)
\(92 = \sqrt{\sqrt{6^{8}}} + 56 \)
\(93 = 5! - \frac{ \sqrt{6^{6}} }{ 8 }\)
\(94 = 6 \cdot 6 + 58 \)
\(95 = \frac{ \sqrt{6 \cdot 6}! }{ 8 } + 5 \)
\(96 = \frac{ 5! \cdot 6 }{ 8 } + 6 \)
\(97 = 85 + 6 + 6 \)
\(98 = 5 \cdot 6 + 68 \)
\(99 = \frac{ 5! + 6! }{ 8 } - 6 \)
\(100 = ( 6 + 6 + 8 ) \cdot 5 \)