All 100 targets have a solution.
\(1 = 17^{4 - 4 }\)
\(2 = 4 - \frac{ 14 }{ 7 }\)
\(3 = \frac{ \sqrt{441} }{ 7 }\)
\(4 = \frac{ 14 \cdot \sqrt{4} }{ 7 }\)
\(5 = \sqrt{144} - 7 \)
\(6 = 47 - 41 \)
\(7 = \sqrt{14 \cdot 4 - 7 }\)
\(8 = \frac{ 14 \cdot 4 }{ 7 }\)
\(9 = 17 - 4 - 4 \)
\(10 = 41 - 4! - 7 \)
\(11 = 14 + 4 - 7 \)
\(12 = \frac{ 41 + 7 }{ 4 }\)
\(13 = 41 - 4 \cdot 7 \)
\(14 = \sqrt{441} - 7 \)
\(15 = 17 - 4 + \sqrt{4 }\)
\(16 = ( \frac{ 14 }{ 7 } )^{4 }\)
\(17 = 14 - 4 + 7 \)
\(18 = \frac{ 4 }{ 4 } + 17 \)
\(19 = \sqrt{144} + 7 \)
\(20 = ( 7 - 4 )! + 14 \)
\(21 = \sqrt{417 + 4 !}\)
\(22 = 4! - \frac{ 14 }{ 7 }\)
\(23 = 14 + \sqrt{4} + 7 \)
\(24 = 41 - 4! + 7 \)
\(25 = 14 + 4 + 7 \)
\(26 = \frac{ 14 }{ 7 } + 4 !\)
\(27 = 44 - 17 \)
\(28 = \sqrt{441} + 7 \)
\(29 = 1^{4} + 4 \cdot 7 \)
\(30 = 41 - 4 - 7 \)
\(31 = 14 + 4! - 7 \)
\(32 = 41 - \sqrt{4} - 7 \)
\(33 = 47 - 14 \)
\(34 = \frac{ 17 \cdot 4 }{ \sqrt{4 } }\)
\(35 = \frac{ 7! }{ 144 }\)
\(36 = 44 - 1 - 7 \)
\(37 = 44 \cdot 1 - 7 \)
\(38 = 41 + 4 - 7 \)
\(39 = ( 1 + 4 ) \cdot 7 + 4 \)
\(40 = ( 4 - 1 + 7 ) \cdot 4 \)
\(41 = 47 - ( 4 - 1 )!\)
\(42 = ( 7 - 4 ) \cdot 14 \)
\(43 = 44 - 1^{7 }\)
\(44 = 41 - 4 + 7 \)
\(45 = 1^{7} + 44 \)
\(46 = 47 - 1^{4 }\)
\(47 = 1^{4} \cdot 47 \)
\(48 = 1^{4} + 47 \)
\(49 = 14 \cdot 4 - 7 \)
\(50 = 44 - 1 + 7 \)
\(51 = 44 \cdot 1 + 7 \)
\(52 = ( 17 - 4 ) \cdot 4 \)
\(53 = ( 4 - 1 )! + 47 \)
\(54 = ( 4 \cdot 7 - 1 ) \cdot \sqrt{4 }\)
\(55 = 71 - 4 \cdot 4 \)
\(56 = ( 1 \cdot 4 + 4 ) \cdot 7 \)
\(57 = 4^{4 - 1} - 7 \)
\(58 = 41 + 4! - 7 \)
\(59 = 71 - \frac{ 4! }{ \sqrt{4 } }\)
\(60 = 74 - 14 \)
\(61 = 14 + 47 \)
\(62 = ( ( 1 \cdot 4 )! + 7 ) \cdot \sqrt{4 }\)
\(63 = \frac{ 441 }{ 7 }\)
\(64 = 17 \cdot 4 - 4 \)
\(65 = 71 - 4 - \sqrt{4 }\)
\(66 = 17 \cdot 4 - \sqrt{4 }\)
\(67 = 71 - \sqrt{4 \cdot 4 }\)
\(68 = \sqrt{4 \cdot 4} \cdot 17 \)
\(69 = 4 \cdot 7 + 41 \)
\(70 = ( 14 - 4 ) \cdot 7 \)
\(71 = 71 - 4 + 4 \)
\(72 = 17 \cdot 4 + 4 \)
\(73 = 74 - 1^{4 }\)
\(74 = 1^{4} \cdot 74 \)
\(75 = 1^{4} + 74 \)
\(76 = ( 17 + \sqrt{4} ) \cdot 4 \)
\(77 = 74 - 1 + 4 \)
\(78 = 74 \cdot 1 + 4 \)
\(79 = 71 + 4 + 4 \)
\(80 = ( 4 - 1 )! + 74 \)
\(81 = ( 7 - 1 \cdot 4 )^{4 }\)
\(82 = ( 7 - 4 )^{4} + 1 \)
\(83 = \frac{ 4! }{ \sqrt{4} } + 71 \)
\(84 = \sqrt{144} \cdot 7 \)
\(85 = ( 4! - 1 ) \cdot 4 - 7 \)
\(86 = \frac{ \sqrt{\sqrt{\sqrt{7^{4!}}}} + 1 }{ 4 }\)
\(87 = \frac{ 174 }{ \sqrt{4 } }\)
\(88 = 14 + 74 \)
\(89 = 41 \cdot \sqrt{4} + 7 \)
\(90 = \frac{ 7! }{ 14 \cdot 4 }\)
\(91 = 71 - 4 + 4 !\)
\(92 = 17 \cdot 4 + 4 !\)
\(93 = 47 \cdot \sqrt{4} - 1 \)
\(94 = 14 \cdot 7 - 4 \)
\(95 = 47 \cdot \sqrt{4} + 1 \)
\(96 = 14 \cdot 7 - \sqrt{4 }\)
\(97 = 74 - 1 + 4 !\)
\(98 = 74 \cdot 1 + 4 !\)
\(99 = 71 + 4 + 4 !\)
\(100 = 14 \cdot 7 + \sqrt{4 }\)