99 of 100 targets have a solution.
\(1 = ( 8 - 7 )^{12 }\)
\(2 = \sqrt{\frac{ 72 }{ 18 }}\)
\(3 = \frac{ 81 }{ 27 }\)
\(4 = \frac{ 72 }{ 18 }\)
\(5 = 8 - \frac{ 21 }{ 7 }\)
\(6 = ( \frac{ 81 }{ 27 } )!\)
\(7 = 17 - 2 - 8 \)
\(8 = \frac{ 72 }{ \sqrt{81 } }\)
\(9 = 27 - 18 \)
\(10 = \frac{ 72 }{ 8 } + 1 \)
\(11 = 28 - 17 \)
\(12 = ( 8 - 7 ) \cdot 12 \)
\(13 = 12 - 7 + 8 \)
\(14 = \sqrt{12 - 8} \cdot 7 \)
\(15 = \sqrt{217 + 8 }\)
\(16 = \frac{ 18 }{ 2 } + 7 \)
\(17 = ( 12 - 8 )! - 7 \)
\(18 = 27 - \sqrt{81 }\)
\(19 = 27 \cdot 1 - 8 \)
\(20 = 21 + 7 - 8 \)
\(21 = \frac{ 8 }{ 2 } + 17 \)
\(22 = ( 18 - 7 ) \cdot 2 \)
\(23 = 17 - 2 + 8 \)
\(24 = ( \frac{ 72 }{ 18 } )!\)
\(25 = \sqrt{17^{2}} + 8 \)
\(26 = \frac{ 182 }{ 7 }\)
\(27 = \sqrt{721 + 8 }\)
\(28 = ( 12 - 8 ) \cdot 7 \)
\(29 = 18 \cdot 2 - 7 \)
\(30 = 27 + \sqrt{\sqrt{81 }}\)
\(31 = 7^{2} - 18 \)
\(32 = 2 \cdot 7 + 18 \)
\(33 = 2 \cdot 8 + 17 \)
\(34 = 27 - 1 + 8 \)
\(35 = 7 \cdot 8 - 21 \)
\(36 = \sqrt{18 \cdot 72 }\)
\(37 = \frac{ 81 - 7 }{ 2 }\)
\(38 = \frac{ 78 }{ 2 } - 1 \)
\(39 = \frac{ 78 \cdot 1 }{ 2 }\)
\(40 = ( 12 - 7 ) \cdot 8 \)
\(41 = ( \frac{ 8 }{ 2 } )! + 17 \)
\(42 = 17 \cdot 2 + 8 \)
\(43 = 71 - 28 \)
\(44 = 7 \cdot 8 - 12 \)
\(45 = 17 + 28 \)
\(46 = ( 7 - 1 ) \cdot 8 - 2 \)
\(47 = 8^{2} - 17 \)
\(48 = \sqrt{2^{7} \cdot 18 }\)
\(49 = 7^{\sqrt{12 - 8 }}\)
\(50 = ( 17 + 8 ) \cdot 2 \)
\(51 = ( 8 - 1 ) \cdot 7 + 2 \)
\(52 = 7^{2} + \sqrt{\sqrt{81 }}\)
\(53 = 7 \cdot 8 - 1 - 2 \)
\(54 = 72 - 18 \)
\(55 = 71 - 2 \cdot 8 \)
\(56 = ( 2 - 1 ) \cdot 7 \cdot 8 \)
\(57 = 78 - 21 \)
\(58 = 7^{2} + \sqrt{81 }\)
\(59 = 7 \cdot 8 + 1 + 2 \)
\(60 = ( 7 - 1 ) \cdot ( 2 + 8 )\)
\(61 = 71 - 2 - 8 \)
\(62 = ( 1 + 7 ) \cdot 8 - 2 \)
\(63 = 72 - \sqrt{81 }\)
\(64 = 72 \cdot 1 - 8 \)
\(65 = 82 - 17 \)
\(66 = 78 - 12 \)
\(67 = 7^{2} + 18 \)
\(68 = 7 \cdot 8 + 12 \)
\(69 = 72 - \sqrt{\sqrt{81 }}\)
\(70 = \frac{ ( 8 - 1 )! }{ 72 }\)
\(71 = 72 - 1^{8 }\)
\(72 = 1^{8} \cdot 72 \)
\(73 = 1^{8} + 72 \)
\(74 = 82 - 1 - 7 \)
\(75 = 87 - 12 \)
\(76 = 12 \cdot 7 - 8 \)
\(77 = 7 \cdot 8 + 21 \)
\(78 = ( 2 - 1 ) \cdot 78 \)
\(79 = 72 - 1 + 8 \)
\(80 = 72 \cdot 1 + 8 \)
\(81 = 72 + \sqrt{81 }\)
\(82 = 1^{7} \cdot 82 \)
\(83 = 1^{7} + 82 \)
\(84 = 87 - 1 - 2 \)
\(85 = 87 \cdot 1 - 2 \)
\(86 = 81 - 2 + 7 \)
\(87 = 2 \cdot 8 + 71 \)
\(88 = 82 - 1 + 7 \)
\(89 = \frac{ 178 }{ 2 }\)
\(90 = 12 + 78 \)
\(91 = ( 21 - 8 ) \cdot 7 \)
\(92 = 12 \cdot 7 + 8 \)
\(93 = ( 1 + 2 )! + 87 \)
\(94 = ?\)
\(95 = 2 \cdot 7 + 81 \)
\(96 = ( 7 - 1 ) \cdot 2 \cdot 8 \)
\(97 = \frac{ ( 1 + 2 )!! }{ 8 } + 7 \)
\(98 = ( 8 - 1 ) \cdot 2 \cdot 7 \)
\(99 = 12 + 87 \)
\(100 = ( \sqrt{\sqrt{81}} + 7 )^{2 }\)