All 100 targets have a solution.
\(1 = 12 - 4 - 7 \)
\(2 = \sqrt{7 - \frac{ 12 }{ 4 }}\)
\(3 = \frac{ 24 }{ 1 + 7 }\)
\(4 = 7 - \frac{ 12 }{ 4 }\)
\(5 = \sqrt{42 - 17 }\)
\(6 = 7 - 1^{24 }\)
\(7 = 24 - 17 \)
\(8 = 1^{24} + 7 \)
\(9 = 12 + 4 - 7 \)
\(10 = \frac{ 12 }{ 4 } + 7 \)
\(11 = 17 - 2 - 4 \)
\(12 = \frac{ 21 \cdot 4 }{ 7 }\)
\(13 = 27 - 14 \)
\(14 = 41 - 27 \)
\(15 = 12 - 4 + 7 \)
\(16 = 4 \cdot 7 - 12 \)
\(17 = 24 \cdot 1 - 7 \)
\(18 = 21 + 4 - 7 \)
\(19 = 14 - 2 + 7 \)
\(20 = ( 12 - 7 ) \cdot 4 \)
\(21 = \frac{ 12 }{ 4 } \cdot 7 \)
\(22 = 27 - 1 - 4 \)
\(23 = 12 + 4 + 7 \)
\(24 = 21 - 4 + 7 \)
\(25 = 42 - 17 \)
\(26 = 47 - 21 \)
\(27 = 1^{4} \cdot 27 \)
\(28 = \frac{ 14^{2} }{ 7 }\)
\(29 = 71 - 42 \)
\(30 = 17 \cdot 2 - 4 \)
\(31 = 72 - 41 \)
\(32 = 21 + 4 + 7 \)
\(33 = 2^{4} + 17 \)
\(34 = \frac{ 17 \cdot 4 }{ 2 }\)
\(35 = 47 - 12 \)
\(36 = ( 7 - 4 ) \cdot 12 \)
\(37 = \frac{ 74 \cdot 1 }{ 2 }\)
\(38 = 17 \cdot 2 + 4 \)
\(39 = 17 - 2 + 4 !\)
\(40 = 4 \cdot 7 + 12 \)
\(41 = 14 + 27 \)
\(42 = ( 14 + 7 ) \cdot 2 \)
\(43 = \frac{ 172 }{ 4 }\)
\(44 = 47 - 1 - 2 \)
\(45 = 47 \cdot 1 - 2 \)
\(46 = 41 - 2 + 7 \)
\(47 = 71 - 24 \)
\(48 = 42 - 1 + 7 \)
\(49 = \frac{ 14 }{ 2 } \cdot 7 \)
\(50 = 41 + 2 + 7 \)
\(51 = 27 \cdot 1 + 4 !\)
\(52 = 21 + 4! + 7 \)
\(53 = 74 - 21 \)
\(54 = 27 \cdot 1 \cdot \sqrt{4 }\)
\(55 = 12 \cdot 4 + 7 \)
\(56 = ( 12 - 4 ) \cdot 7 \)
\(57 = 4^{1 + 2} - 7 \)
\(58 = 72 - 14 \)
\(59 = 12 + 47 \)
\(60 = ( 17 - 2 ) \cdot 4 \)
\(61 = 7^{\sqrt{4}} + 12 \)
\(62 = 74 - 12 \)
\(63 = 7^{2} + 14 \)
\(64 = 4^{\frac{ 21 }{ 7 }}\)
\(65 = 71 - 2 - 4 \)
\(66 = 17 \cdot 4 - 2 \)
\(67 = 72 - 1 - 4 \)
\(68 = 21 + 47 \)
\(69 = 71 + 2 - 4 \)
\(70 = ( 7 - 2 ) \cdot 14 \)
\(71 = 72 - 1^{4 }\)
\(72 = 1^{4} \cdot 72 \)
\(73 = 71 - 2 + 4 \)
\(74 = ( 2 - 1 ) \cdot 74 \)
\(75 = 41 \cdot 2 - 7 \)
\(76 = ( 12 + 7 ) \cdot 4 \)
\(77 = 21 \cdot 4 - 7 \)
\(78 = ( 4 - 1 )! + 72 \)
\(79 = 2 \cdot 4 + 71 \)
\(80 = 12 \cdot 7 - 4 \)
\(81 = ( \frac{ 21 }{ 7 } )^{4 }\)
\(82 = 12 \cdot 7 - \sqrt{4 }\)
\(83 = \frac{ 4! }{ 2 } + 71 \)
\(84 = ( 14 - 2 ) \cdot 7 \)
\(85 = \frac{ 4! }{ 2 } \cdot 7 + 1 \)
\(86 = 12 + 74 \)
\(87 = \frac{ 174 }{ 2 }\)
\(88 = 12 \cdot 7 + 4 \)
\(89 = 41 \cdot 2 + 7 \)
\(90 = 7^{2} + 41 \)
\(91 = 21 \cdot 4 + 7 \)
\(92 = ( 47 - 1 ) \cdot 2 \)
\(93 = 47 \cdot 2 - 1 \)
\(94 = 47 \cdot 1 \cdot 2 \)
\(95 = 21 + 74 \)
\(96 = 14 \cdot 7 - 2 \)
\(97 = 71 + 2 + 4 !\)
\(98 = ( 12 + \sqrt{4} ) \cdot 7 \)
\(99 = ( 7 - \sqrt{4} )! - 21 \)
\(100 = 14 \cdot 7 + 2 \)