All 100 targets have a solution.
\(1 = 13^{4 - 4 }\)
\(2 = 43 - 41 \)
\(3 = 4 \cdot 4 - 13 \)
\(4 = \frac{ \sqrt{144} }{ 3 }\)
\(5 = 13 - 4 - 4 \)
\(6 = \frac{ 14 + 4 }{ 3 }\)
\(7 = 41 - 34 \)
\(8 = 14 - 3 \cdot \sqrt{4 }\)
\(9 = \sqrt{144} - 3 \)
\(10 = \frac{ 14 }{ \sqrt{4} } + 3 \)
\(11 = \frac{ 41 + 3 }{ 4 }\)
\(12 = 13 - \frac{ 4 }{ 4 }\)
\(13 = 44 - 31 \)
\(14 = \frac{ 4 }{ 4 } + 13 \)
\(15 = \sqrt{144} + 3 \)
\(16 = 14 + 3! - 4 \)
\(17 = \sqrt{4 \cdot 4} + 13 \)
\(18 = \sqrt{441} - 3 \)
\(19 = 13 + \sqrt{4} + 4 \)
\(20 = 34 - 14 \)
\(21 = 13 + 4 + 4 \)
\(22 = \frac{ 44 }{ 3 - 1 }\)
\(23 = 31 - 4 - 4 \)
\(24 = \frac{ 144 }{ 3 ! }\)
\(25 = 14 \cdot \sqrt{4} - 3 \)
\(26 = 3 \cdot 4 + 14 \)
\(27 = \sqrt{441} + 3 !\)
\(28 = 13 \cdot 4 - 4 !\)
\(29 = 43 - 14 \)
\(30 = ( 14 - 4 ) \cdot 3 \)
\(31 = 44 - 13 \)
\(32 = \frac{ 4 }{ 4 } + 31 \)
\(33 = 34 - 1^{4 }\)
\(34 = 1^{4} \cdot 34 \)
\(35 = 1^{4} + 34 \)
\(36 = \sqrt{144} \cdot 3 \)
\(37 = 34 - 1 + 4 \)
\(38 = 14 \cdot 3 - 4 \)
\(39 = 31 + 4 + 4 \)
\(40 = 41 + 3 - 4 \)
\(41 = ( 4 - 3 ) \cdot 41 \)
\(42 = 41 - 3 + 4 \)
\(43 = 1^{4} \cdot 43 \)
\(44 = ( 14 - 3 ) \cdot 4 \)
\(45 = 1^{3} + 44 \)
\(46 = 14 \cdot 3 + 4 \)
\(47 = 4 \cdot 4 + 31 \)
\(48 = \frac{ 144 }{ 3 }\)
\(49 = \sqrt{4}^{3} + 41 \)
\(50 = 4^{3} - 14 \)
\(51 = 31 - 4 + 4 !\)
\(52 = \sqrt{4 \cdot 4} \cdot 13 \)
\(53 = 14 \cdot 4 - 3 \)
\(54 = ( 14 + 4 ) \cdot 3 \)
\(55 = \sqrt{4 \cdot 4}! + 31 \)
\(56 = 13 \cdot 4 + 4 \)
\(57 = 13 + 44 \)
\(58 = 3 \cdot 4! - 14 \)
\(59 = 14 \cdot 4 + 3 \)
\(60 = ( 13 + \sqrt{4} ) \cdot 4 \)
\(61 = 4^{3} + 1 - 4 \)
\(62 = 14 \cdot 4 + 3 !\)
\(63 = \sqrt{441} \cdot 3 \)
\(64 = 4^{\sqrt{13 - 4 }}\)
\(65 = 4 \cdot 4! - 31 \)
\(66 = 14 \cdot 3 + 4 !\)
\(67 = \frac{ 134 }{ \sqrt{4 } }\)
\(68 = ( 13 + 4 ) \cdot 4 \)
\(69 = \frac{ 414 }{ 3 ! }\)
\(70 = ( 3 + \sqrt{4} ) \cdot 14 \)
\(71 = 41 + 3! + 4 !\)
\(72 = \sqrt{144} \cdot 3 !\)
\(73 = ( 4! - 1 ) \cdot 3 + 4 \)
\(74 = ( 13 + 4! ) \cdot \sqrt{4 }\)
\(75 = 31 + 44 \)
\(76 = 13 \cdot 4 + 4 !\)
\(77 = ( 1 + 4 )! - 43 \)
\(78 = 4^{3} + 14 \)
\(79 = 41 \cdot \sqrt{4} - 3 \)
\(80 = ( 14 + 3! ) \cdot 4 \)
\(81 = \sqrt{13 - 4}^{4 }\)
\(82 = ( 3! - 4 ) \cdot 41 \)
\(83 = 4 \cdot 4! - 13 \)
\(84 = 41 + 43 \)
\(85 = 41 \cdot \sqrt{4} + 3 \)
\(86 = 3 \cdot 4! + 14 \)
\(87 = 43 \cdot \sqrt{4} + 1 \)
\(88 = ( 3 - 1 ) \cdot 44 \)
\(89 = 4^{3} + 1 + 4 !\)
\(90 = \frac{ ( 1 + 4 )! \cdot 3 }{ 4 }\)
\(91 = 4 \cdot 4! + 1 - 3 !\)
\(92 = ( 4! - 1^{3} ) \cdot 4 \)
\(93 = 1 \cdot 4 \cdot 4! - 3 \)
\(94 = ( 41 + 3! ) \cdot \sqrt{4 }\)
\(95 = 3^{4} + 14 \)
\(96 = ( 14 + \sqrt{4} ) \cdot 3 !\)
\(97 = ( 1 + 4! ) \cdot 4 - 3 \)
\(98 = ( 3 + 4 ) \cdot 14 \)
\(99 = 41 \cdot 3 - 4 !\)
\(100 = 31 \cdot 4 - 4 !\)