All 100 targets have a solution.
\(1 = ( 8 - 7 )^{13 }\)
\(2 = 8 - ( 13 - 7 )\)
\(3 = \frac{ 13 + 8 }{ 7 }\)
\(4 = 7 - \frac{ 18 }{ 3 ! }\)
\(5 = 18 - 3! - 7 \)
\(6 = \frac{ 78 }{ 13 }\)
\(7 = 3 \cdot 8 - 17 \)
\(8 = 81 - 73 \)
\(9 = \frac{ 73 - 1 }{ 8 }\)
\(10 = \sqrt{13 + 87 }\)
\(11 = 7 - ( 1 + 3 ) + 8 \)
\(12 = 83 - 71 \)
\(13 = ( 8 - 7 ) \cdot 13 \)
\(14 = 13 - 7 + 8 \)
\(15 = 17 + 3! - 8 \)
\(16 = 31 - 7 - 8 \)
\(17 = 18 + 3! - 7 \)
\(18 = ( 7 - 3! ) \cdot 18 \)
\(19 = 37 - 18 \)
\(20 = \frac{ 81 }{ 3 } - 7 \)
\(21 = 38 - 17 \)
\(22 = 17 - 3 + 8 \)
\(23 = \sqrt{8^{3} + 17 }\)
\(24 = 3! \cdot 7 - 18 \)
\(25 = 7 \cdot 8 - 31 \)
\(26 = \frac{ 78 \cdot 1 }{ 3 }\)
\(27 = ( 17 - 8 ) \cdot 3 \)
\(28 = \sqrt{781 + 3 }\)
\(29 = 37 \cdot 1 - 8 \)
\(30 = 31 + 7 - 8 \)
\(31 = ( 8 - 7 ) \cdot 31 \)
\(32 = 31 - 7 + 8 \)
\(33 = 71 - 38 \)
\(34 = \frac{ 81 }{ 3 } + 7 \)
\(35 = ( 13 - 8 ) \cdot 7 \)
\(36 = 37 - 1^{8 }\)
\(37 = 1^{8} \cdot 37 \)
\(38 = 1^{8} + 37 \)
\(39 = 3 \cdot 7 + 18 \)
\(40 = 37 + \sqrt{\sqrt{81 }}\)
\(41 = 3 \cdot 8 + 17 \)
\(42 = \frac{ 18 }{ 3 } \cdot 7 \)
\(43 = 7 \cdot 8 - 13 \)
\(44 = 81 - 37 \)
\(45 = 37 \cdot 1 + 8 \)
\(46 = 37 + \sqrt{81 }\)
\(47 = 78 - 31 \)
\(48 = ( 13 - 7 ) \cdot 8 \)
\(49 = ( 8 - 3 )! - 71 \)
\(50 = ( 1 \cdot 3 )! \cdot 7 + 8 \)
\(51 = ( 7 - 1 ) \cdot 8 + 3 \)
\(52 = ( 8 - 1 ) \cdot 7 + 3 \)
\(53 = 1 \cdot 7 \cdot 8 - 3 \)
\(54 = ( 17 - 8 ) \cdot 3 !\)
\(55 = 17 + 38 \)
\(56 = 87 - 31 \)
\(57 = 71 - 3! - 8 \)
\(58 = 7 \cdot 8 - 1 + 3 \)
\(59 = 17 \cdot 3 + 8 \)
\(60 = 71 - 3 - 8 \)
\(61 = 18 \cdot 3 + 7 \)
\(62 = \sqrt{\sqrt{7^{8}}} + 13 \)
\(63 = 87 - ( 1 + 3 )!\)
\(64 = 73 - \sqrt{81 }\)
\(65 = 78 - 13 \)
\(66 = 83 - 17 \)
\(67 = 73 - \sqrt{\sqrt{81 }}!\)
\(68 = 81 - 3! - 7 \)
\(69 = 7 \cdot 8 + 13 \)
\(70 = 73 - \sqrt{\sqrt{81 }}\)
\(71 = 81 - 3 - 7 \)
\(72 = ( 7 - 3 ) \cdot 18 \)
\(73 = 1^{8} \cdot 73 \)
\(74 = 87 - 13 \)
\(75 = ( 17 + 8 ) \cdot 3 \)
\(76 = 71 - 3 + 8 \)
\(77 = 78 - 1^{3 }\)
\(78 = 1^{3} \cdot 78 \)
\(79 = 1^{3} + 78 \)
\(80 = 73 - 1 + 8 \)
\(81 = 73 \cdot 1 + 8 \)
\(82 = 73 + \sqrt{81 }\)
\(83 = 13 \cdot 7 - 8 \)
\(84 = 1^{7} + 83 \)
\(85 = ( 8 - 3 ) \cdot 17 \)
\(86 = 87 - 1^{3 }\)
\(87 = 7 \cdot 8 + 31 \)
\(88 = 1^{3} + 87 \)
\(89 = 83 - 1 + 7 \)
\(90 = 83 \cdot 1 + 7 \)
\(91 = 13 + 78 \)
\(92 = 87 - 1 + 3 !\)
\(93 = 87 \cdot 1 + 3 !\)
\(94 = 17 \cdot 3! - 8 \)
\(95 = 3 \cdot 8 + 71 \)
\(96 = ( \sqrt{81} + 7 ) \cdot 3 !\)
\(97 = 13 \cdot 8 - 7 \)
\(98 = \sqrt{3^{8}} + 17 \)
\(99 = 13 \cdot 7 + 8 \)
\(100 = 13 + 87 \)