99 of 100 targets have a solution.
\(1 = 87 - 86 \)
\(2 = 8 - ( 8 - 7 ) \cdot 6 \)
\(3 = 67 - 8 \cdot 8 \)
\(4 = \frac{ 8 }{ \frac{ 6 + 8 }{ 7 } }\)
\(5 = \frac{ 78 }{ 6 } - 8 \)
\(6 = ( 67 - 8 \cdot 8 )!\)
\(7 = 8 - ( 7 - 6 )^{8 }\)
\(8 = 86 - 78 \)
\(9 = \frac{ 78 - 6 }{ 8 }\)
\(10 = 78 - 68 \)
\(11 = \frac{ 8 }{ 8 - 6 } + 7 \)
\(12 = 88 - 76 \)
\(13 = 6 + 7 - 8 + 8 \)
\(14 = ( 8 - 7 ) \cdot 6 + 8 \)
\(15 = \sqrt{88 - 7} + 6 \)
\(16 = \frac{ 6 + 8 }{ 7 } \cdot 8 \)
\(17 = \sqrt{87 - 6} + 8 \)
\(18 = \sqrt{\sqrt{88 - 7}} \cdot 6 \)
\(19 = 87 - 68 \)
\(20 = \frac{ ( 7 + 8 ) \cdot 8 }{ 6 }\)
\(21 = 88 - 67 \)
\(22 = \sqrt{68 \cdot 7 + 8 }\)
\(23 = ( 8 - 6 ) \cdot 8 + 7 \)
\(24 = \sqrt{( 78 - 6 ) \cdot 8 }\)
\(25 = \sqrt{6! - 87 - 8 }\)
\(26 = 6 \cdot 7 - 8 - 8 \)
\(27 = \sqrt{\sqrt{\sqrt{88 - 7}}^{6 }}\)
\(28 = \frac{ 8 }{ 8 - 6 } \cdot 7 \)
\(29 = 6 + 7 + 8 + 8 \)
\(30 = 78 - 6 \cdot 8 \)
\(31 = 87 - \frac{ 8! }{ 6 ! }\)
\(32 = \sqrt{( 8 - 6 )^{7} \cdot 8 }\)
\(33 = 6 \cdot 8 - 7 - 8 \)
\(34 = \sqrt{8 + 8} \cdot 7 + 6 \)
\(35 = ( 6 - \frac{ 8 }{ 8 } ) \cdot 7 \)
\(36 = ( 7 - \frac{ 8 }{ 8 } ) \cdot 6 \)
\(37 = 86 - \sqrt{\sqrt{7^{8 }}}\)
\(38 = \frac{ 76 }{ \sqrt{\sqrt{8 + 8 }} }\)
\(39 = \frac{ 78 }{ 8 - 6 }\)
\(40 = ( 6 + 7 - 8 ) \cdot 8 \)
\(41 = 7^{8 - 6} - 8 \)
\(42 = 6 \cdot 7 - 8 + 8 \)
\(43 = 6 \cdot 7 + \frac{ 8 }{ 8 }\)
\(44 = 6 \cdot 7 + \sqrt{\sqrt{8 + 8 }}\)
\(45 = \frac{ \frac{ 7! }{ 6 + 8 } }{ 8 }\)
\(46 = 88 - 6 \cdot 7 \)
\(47 = 6 \cdot 8 + 7 - 8 \)
\(48 = ( 8 - 7 ) \cdot 6 \cdot 8 \)
\(49 = 6 \cdot 8 - 7 + 8 \)
\(50 = \sqrt{8 \cdot 8} \cdot 7 - 6 \)
\(51 = 67 - 8 - 8 \)
\(52 = 76 - \sqrt{8 + 8 }!\)
\(53 = 68 - 7 - 8 \)
\(54 = \sqrt{88 - 7} \cdot 6 \)
\(55 = \sqrt{8 \cdot 8} \cdot 6 + 7 \)
\(56 = ( 8 - ( 7 - 6 ) ) \cdot 8 \)
\(57 = 7^{8 - 6} + 8 \)
\(58 = 6 \cdot 7 + 8 + 8 \)
\(59 = 67 - \sqrt{8 \cdot 8 }\)
\(60 = 76 - 8 - 8 \)
\(61 = \sqrt{\sqrt{\sqrt{( 68 - 7 )^{8 }}}}\)
\(62 = \sqrt{8 \cdot 8} \cdot 7 + 6 \)
\(63 = 67 - \sqrt{8 + 8 }\)
\(64 = 78 - 6 - 8 \)
\(65 = 8 \cdot 8 - 6 + 7 \)
\(66 = 67 - \frac{ 8 }{ 8 }\)
\(67 = 67 - 8 + 8 \)
\(68 = 788 - 6 !\)
\(69 = 68 - 7 + 8 \)
\(70 = 7 \cdot 8 + 6 + 8 \)
\(71 = 86 - 7 - 8 \)
\(72 = 76 - \sqrt{8 + 8 }\)
\(73 = 87 - 6 - 8 \)
\(74 = \frac{ 7! - 8 }{ 68 }\)
\(75 = 76 - \frac{ 8 }{ 8 }\)
\(76 = 76 - 8 + 8 \)
\(77 = \frac{ 8 }{ 8 } + 76 \)
\(78 = \sqrt{78^{8 - 6 }}\)
\(79 = \sqrt{\sqrt{\sqrt{( 86 - 7 )^{8 }}}}\)
\(80 = 78 - 6 + 8 \)
\(81 = 88 - \frac{ 7! }{ 6 ! }\)
\(82 = ( 7 + 8 ) \cdot 6 - 8 \)
\(83 = 67 + 8 + 8 \)
\(84 = \frac{ 7! }{ 68 - 8 }\)
\(85 = 86 + 7 - 8 \)
\(86 = ( 8 - 7 ) \cdot 86 \)
\(87 = 86 - 7 + 8 \)
\(88 = ( 7 - 6 ) \cdot 88 \)
\(89 = 87 - 6 + 8 \)
\(90 = ( 6 + 8 ) \cdot 7 - 8 \)
\(91 = \sqrt{8 + 8}! + 67 \)
\(92 = 76 + 8 + 8 \)
\(93 = \sqrt{\sqrt{\sqrt{( 86 + 7 )^{8 }}}}\)
\(94 = \frac{ 8! }{ 7! } + 86 \)
\(95 = \frac{ 7! }{ 6! } + 88 \)
\(96 = \frac{ 768 }{ 8 }\)
\(97 = \frac{ \frac{ 7! }{ 6 } }{ 8 } - 8 \)
\(98 = ( 7 + 8 ) \cdot 6 + 8 \)
\(99 = ?\)
\(100 = \sqrt{8 + 8}! + 76 \)