All 100 targets have a solution.
\(1 = 8 - ( 12 - 5 )\)
\(2 = \frac{ 21 - 5 }{ 8 }\)
\(3 = \frac{ 25 - 1 }{ 8 }\)
\(4 = \frac{ 12 + 8 }{ 5 }\)
\(5 = 15 - 2 - 8 \)
\(6 = \frac{ 18 }{ 5 - 2 }\)
\(7 = 25 - 18 \)
\(8 = 128 - 5 !\)
\(9 = 12 + 5 - 8 \)
\(10 = \sqrt{12 - 8} \cdot 5 \)
\(11 = 15 - \frac{ 8 }{ 2 }\)
\(12 = \sqrt{152 - 8 }\)
\(13 = 28 - 15 \)
\(14 = ( 15 - 8 ) \cdot 2 \)
\(15 = 12 - 5 + 8 \)
\(16 = 25 - \sqrt{81 }\)
\(17 = 25 \cdot 1 - 8 \)
\(18 = 21 + 5 - 8 \)
\(19 = \frac{ 152 }{ 8 }\)
\(20 = ( 12 - 8 ) \cdot 5 \)
\(21 = 15 - 2 + 8 \)
\(22 = 15 \cdot 2 - 8 \)
\(23 = 51 - 28 \)
\(24 = 21 - 5 + 8 \)
\(25 = 12 + 5 + 8 \)
\(26 = ( 18 - 5 ) \cdot 2 \)
\(27 = 28 - 1^{5 }\)
\(28 = 5 \cdot 8 - 12 \)
\(29 = 81 - 52 \)
\(30 = \frac{ 58 }{ 2 } + 1 \)
\(31 = 82 - 51 \)
\(32 = 25 - 1 + 8 \)
\(33 = 25 \cdot 1 + 8 \)
\(34 = 52 - 18 \)
\(35 = 51 - 2 \cdot 8 \)
\(36 = ( 8 - 5 ) \cdot 12 \)
\(37 = 58 - 21 \)
\(38 = 15 \cdot 2 + 8 \)
\(39 = \sqrt{25}! - 81 \)
\(40 = \sqrt{25} \cdot 1 \cdot 8 \)
\(41 = 18 \cdot 2 + 5 \)
\(42 = \frac{ 85 - 1 }{ 2 }\)
\(43 = 15 + 28 \)
\(44 = 52 \cdot 1 - 8 \)
\(45 = \sqrt{25 \cdot 81 }\)
\(46 = 58 - 12 \)
\(47 = 51 - \frac{ 8 }{ 2 }\)
\(48 = \frac{ ( 8 - 2 )! }{ 15 }\)
\(49 = ( 15 - 8 )^{2 }\)
\(50 = 2^{5} + 18 \)
\(51 = 52 - 1^{8 }\)
\(52 = 12 \cdot 5 - 8 \)
\(53 = 1^{8} + 52 \)
\(54 = ( 5 - 2 ) \cdot 18 \)
\(55 = \frac{ 8 }{ 2 } + 51 \)
\(56 = 81 - 25 \)
\(57 = 51 - 2 + 8 \)
\(58 = ( 2 - 1 ) \cdot 58 \)
\(59 = 52 - 1 + 8 \)
\(60 = \frac{ 15 \cdot 8 }{ 2 }\)
\(61 = 52 + \sqrt{81 }\)
\(62 = 182 - 5 !\)
\(63 = ( 8 - 5 ) \cdot 21 \)
\(64 = \frac{ 512 }{ 8 }\)
\(65 = ( 21 - 8 ) \cdot 5 \)
\(66 = 8^{\sqrt{5 - 1}} + 2 \)
\(67 = 82 - 15 \)
\(68 = 12 \cdot 5 + 8 \)
\(69 = \frac{ 18 + 5! }{ 2 }\)
\(70 = 12 + 58 \)
\(71 = 81 - 2 \cdot 5 \)
\(72 = ( 8 - 5 )! \cdot 12 \)
\(73 = 85 - 12 \)
\(74 = 81 - 2 - 5 \)
\(75 = 25 \cdot \sqrt{\sqrt{81 }}\)
\(76 = 81 - \sqrt{25 }\)
\(77 = 82 \cdot 1 - 5 \)
\(78 = 81 + 2 - 5 \)
\(79 = \frac{ 158 }{ 2 }\)
\(80 = ( 18 - 2 ) \cdot 5 \)
\(81 = 82 - 1^{5 }\)
\(82 = 1^{5} \cdot 82 \)
\(83 = 1^{5} + 82 \)
\(84 = 81 - 2 + 5 \)
\(85 = ( 2 - 1 ) \cdot 85 \)
\(86 = \sqrt{25} + 81 \)
\(87 = 82 \cdot 1 + 5 \)
\(88 = 18 \cdot 5 - 2 \)
\(89 = \frac{ ( 5 - 2 )!! }{ 8 } - 1 \)
\(90 = 18 \cdot \sqrt{25 }\)
\(91 = 12 \cdot 8 - 5 \)
\(92 = 18 \cdot 5 + 2 \)
\(93 = 5! - ( 28 - 1 )\)
\(94 = 51 \cdot 2 - 8 \)
\(95 = 5! - ( ( \frac{ 8 }{ 2 } )! + 1 )\)
\(96 = ( 1 + 5 ) \cdot 2 \cdot 8 \)
\(97 = 12 + 85 \)
\(98 = 218 - 5 !\)
\(99 = \sqrt{\sqrt{( 2 \cdot 5 )^{8}}} - 1 \)
\(100 = ( 12 + 8 ) \cdot 5 \)