99 of 100 targets have a solution.
\(1 = 8 - ( 15 - 8 )\)
\(2 = \sqrt{85 - 81 }\)
\(3 = \frac{ 18 }{ ( 8 - 5 )! }\)
\(4 = 85 - 81 \)
\(5 = 18 - 5 - 8 \)
\(6 = \frac{ 18 }{ 8 - 5 }\)
\(7 = \sqrt{58 - \sqrt{81 }}\)
\(8 = ( 1^{5} )^{8} \cdot 8 \)
\(9 = ( 1^{5} )^{8} + 8 \)
\(10 = \frac{ 8 }{ 5 - 1 } + 8 \)
\(11 = 15 - \sqrt{8 + 8 }\)
\(12 = \frac{ 5! }{ 18 - 8 }\)
\(13 = 8 \cdot 8 - 51 \)
\(14 = 15 - \frac{ 8 }{ 8 }\)
\(15 = 15 - 8 + 8 \)
\(16 = \frac{ 8 }{ 8 } + 15 \)
\(17 = \sqrt{18 \cdot 8} + 5 \)
\(18 = \sqrt{5 - 1} + 8 + 8 \)
\(19 = \sqrt{8 + 8} + 15 \)
\(20 = \sqrt{51 \cdot 8 - 8 }\)
\(21 = 18 - 5 + 8 \)
\(22 = 5 \cdot 8 - 18 \)
\(23 = 81 - 58 \)
\(24 = ( 85 - 81 )!\)
\(25 = 5^{\frac{ 8 }{ 8 } + 1 }\)
\(26 = 5^{\sqrt{\sqrt{8 + 8}}} + 1 \)
\(27 = \frac{ 81 }{ 8 - 5 }\)
\(28 = \sqrt{\sqrt{( 1 + 5 )^{8}}} - 8 \)
\(29 = \sqrt{\sqrt{81}} \cdot 8 + 5 \)
\(30 = \sqrt{\sqrt{8 + 8}} \cdot 15 \)
\(31 = 15 + 8 + 8 \)
\(32 = ( \sqrt{81} - 5 ) \cdot 8 \)
\(33 = \frac{ 5! }{ 8 } + 18 \)
\(34 = \sqrt{\sqrt{5^{8}}} + \sqrt{81 }\)
\(35 = 51 - 8 - 8 \)
\(36 = \sqrt{\sqrt{( 1^{8} + 5 )^{8 }}}\)
\(37 = 88 - 51 \)
\(38 = \sqrt{\sqrt{81}}! \cdot 5 + 8 \)
\(39 = 5 \cdot 8 - 1^{8 }\)
\(40 = 58 - 18 \)
\(41 = 81 - 5 \cdot 8 \)
\(42 = ( 8 - 1 ) \cdot ( 8 - 5 )!\)
\(43 = 51 - \sqrt{8 \cdot 8 }\)
\(44 = \frac{ 88 }{ \sqrt{5 - 1 } }\)
\(45 = ( 1^{8} + 8 ) \cdot 5 \)
\(46 = 5 \cdot 8 + \sqrt{\sqrt{81 }}!\)
\(47 = 51 - \sqrt{8 + 8 }\)
\(48 = ( 1^{8} + 5 ) \cdot 8 \)
\(49 = 58 - \sqrt{81 }\)
\(50 = ( 18 - 8 ) \cdot 5 \)
\(51 = 51 - 8 + 8 \)
\(52 = \frac{ 8 }{ 8 } + 51 \)
\(53 = \sqrt{81} \cdot 5 + 8 \)
\(54 = ( 8 - 5 ) \cdot 18 \)
\(55 = 58 - \sqrt{\sqrt{81 }}\)
\(56 = ( 15 - 8 ) \cdot 8 \)
\(57 = 58 - 1^{8 }\)
\(58 = 5 \cdot 8 + 18 \)
\(59 = 1^{8} + 58 \)
\(60 = \sqrt{8 + 8} \cdot 15 \)
\(61 = 58 + \sqrt{\sqrt{81 }}\)
\(62 = 8 \cdot 8 - \sqrt{5 - 1 }\)
\(63 = 8 \cdot 8 - 1^{5 }\)
\(64 = 88 - ( 5 - 1 )!\)
\(65 = 58 - 1 + 8 \)
\(66 = 58 \cdot 1 + 8 \)
\(67 = 85 - 18 \)
\(68 = 188 - 5 !\)
\(69 = 1 \cdot 8 \cdot 8 + 5 \)
\(70 = 8 \cdot 8 + 1 + 5 \)
\(71 = \sqrt{1^{5} + \frac{ 8! }{ 8 }}\)
\(72 = ( 1^{5} + 8 ) \cdot 8 \)
\(73 = 88 - 15 \)
\(74 = ?\)
\(75 = 81 - ( 8 - 5 )!\)
\(76 = 18 + 58 \)
\(77 = 85 \cdot 1 - 8 \)
\(78 = 81 + 5 - 8 \)
\(79 = 8 \cdot 8 + 15 \)
\(80 = ( 1 \cdot 8 + 8 ) \cdot 5 \)
\(81 = ( 8 + 8 ) \cdot 5 + 1 \)
\(82 = 18 \cdot 5 - 8 \)
\(83 = 88 \cdot 1 - 5 \)
\(84 = 81 - 5 + 8 \)
\(85 = 1^{8} \cdot 85 \)
\(86 = 1^{8} + 85 \)
\(87 = 88 - 1^{5 }\)
\(88 = 1^{5} \cdot 88 \)
\(89 = 1^{5} + 88 \)
\(90 = \sqrt{5 - 1} + 88 \)
\(91 = \sqrt{\sqrt{81}}! + 85 \)
\(92 = 85 - 1 + 8 \)
\(93 = 85 \cdot 1 + 8 \)
\(94 = \sqrt{81} + 85 \)
\(95 = \frac{ \sqrt{\sqrt{81}}!! }{ 8 } + 5 \)
\(96 = \frac{ 5! }{ 8 } + 81 \)
\(97 = 5! - ( \sqrt{8 + 8}! - 1 )\)
\(98 = 18 \cdot 5 + 8 \)
\(99 = \sqrt{1 + 5!} + 88 \)
\(100 = \sqrt{\sqrt{( \sqrt{5 - 1} + 8 )^{8 }}}\)