99 of 100 targets have a solution.
\(1 = \frac{ 15 - 7 }{ 8 }\)
\(2 = \sqrt{17 - 5 - 8 }\)
\(3 = \sqrt{\frac{ 18 }{ 7 - 5 }}\)
\(4 = 17 - 5 - 8 \)
\(5 = \frac{ 85 }{ 17 }\)
\(6 = 81 - 75 \)
\(7 = \frac{ 57 - 1 }{ 8 }\)
\(8 = \sqrt{( 15 - 7 ) \cdot 8 }\)
\(9 = \frac{ 18 }{ 7 - 5 }\)
\(10 = \sqrt{17 + 8} + 5 \)
\(11 = 17 - ( 8 - 5 )!\)
\(12 = \frac{ 85 - 1 }{ 7 }\)
\(13 = 71 - 58 \)
\(14 = 85 - 71 \)
\(15 = ( 8 - 7 ) \cdot 15 \)
\(16 = 15 - 7 + 8 \)
\(17 = 5 \cdot 7 - 18 \)
\(18 = \sqrt{18^{7 - 5 }}\)
\(19 = \frac{ 57 }{ \sqrt{\sqrt{81 }} }\)
\(20 = 17 - 5 + 8 \)
\(21 = \sqrt{81} + 5 + 7 \)
\(22 = ( 7 - 1 ) \cdot 5 - 8 \)
\(23 = 5 \cdot 8 - 17 \)
\(24 = 81 - 57 \)
\(25 = \frac{ 75 }{ \sqrt{\sqrt{81 }} }\)
\(26 = 5 \cdot 7 - \sqrt{81 }\)
\(27 = 78 - 51 \)
\(28 = \sqrt{785 - 1 }\)
\(29 = ( 7 - \sqrt{\sqrt{81}} )! + 5 \)
\(30 = 15 + 7 + 8 \)
\(31 = 71 - 5 \cdot 8 \)
\(32 = \frac{ 5! }{ 8 } + 17 \)
\(33 = 5! - 87 \cdot 1 \)
\(34 = 5! - ( 87 - 1 )\)
\(35 = 1^{8} \cdot 5 \cdot 7 \)
\(36 = 87 - 51 \)
\(37 = \sqrt{\sqrt{81}}! \cdot 5 + 7 \)
\(38 = \sqrt{81} \cdot 5 - 7 \)
\(39 = 57 - 18 \)
\(40 = 1^{7} \cdot 5 \cdot 8 \)
\(41 = 58 - 17 \)
\(42 = \frac{ \frac{ 7! }{ 15 } }{ 8 }\)
\(43 = 5! - ( 78 - 1 )\)
\(44 = 5 \cdot 7 + \sqrt{81 }\)
\(45 = ( 17 - 8 ) \cdot 5 \)
\(46 = 81 - 5 \cdot 7 \)
\(47 = 1 \cdot 5 \cdot 8 + 7 \)
\(48 = 57 - \sqrt{81 }\)
\(49 = ( 15 - 8 ) \cdot 7 \)
\(50 = 51 + 7 - 8 \)
\(51 = ( 8 - 5 ) \cdot 17 \)
\(52 = 51 - 7 + 8 \)
\(53 = 5 \cdot 7 + 18 \)
\(54 = 57 - \sqrt{\sqrt{81 }}\)
\(55 = ( 18 - 7 ) \cdot 5 \)
\(56 = 57 - 1^{8 }\)
\(57 = 75 - 18 \)
\(58 = 178 - 5 !\)
\(59 = 1^{7} + 58 \)
\(60 = 57 + \sqrt{\sqrt{81 }}\)
\(61 = 1 \cdot 7 \cdot 8 + 5 \)
\(62 = 7 \cdot 8 + 1 + 5 \)
\(63 = 78 - 15 \)
\(64 = ( 15 - 7 ) \cdot 8 \)
\(65 = 57 \cdot 1 + 8 \)
\(66 = 57 + \sqrt{81 }\)
\(67 = 187 - 5 !\)
\(68 = 85 - 17 \)
\(69 = 81 - 5 - 7 \)
\(70 = ( 7 - 1 + 8 ) \cdot 5 \)
\(71 = 7 \cdot 8 + 15 \)
\(72 = 87 - 15 \)
\(73 = 78 \cdot 1 - 5 \)
\(74 = \frac{ 518 }{ 7 }\)
\(75 = 17 + 58 \)
\(76 = 1^{8} + 75 \)
\(77 = 17 \cdot 5 - 8 \)
\(78 = 1^{5} \cdot 78 \)
\(79 = 1^{5} + 78 \)
\(80 = \sqrt{5 - 1} + 78 \)
\(81 = 87 - 1 - 5 \)
\(82 = 75 - 1 + 8 \)
\(83 = \frac{ 581 }{ 7 }\)
\(84 = 75 + \sqrt{81 }\)
\(85 = 1^{7} \cdot 85 \)
\(86 = 1^{7} + 85 \)
\(87 = 1^{5} \cdot 87 \)
\(88 = 1^{5} + 87 \)
\(89 = \sqrt{5 - 1} + 87 \)
\(90 = ( 5 + 8 ) \cdot 7 - 1 \)
\(91 = ( 18 - 5 ) \cdot 7 \)
\(92 = 85 \cdot 1 + 7 \)
\(93 = 15 + 78 \)
\(94 = ?\)
\(95 = 5! - 17 - 8 \)
\(96 = ( 17 - 5 ) \cdot 8 \)
\(97 = 15 \cdot 7 - 8 \)
\(98 = ( \sqrt{81} + 5 ) \cdot 7 \)
\(99 = 5! - \sqrt{\sqrt{81}} \cdot 7 \)
\(100 = \sqrt{\sqrt{7^{8}}} + 51 \)