All 100 targets have a solution.
\(1 = ( 5 - 4 )^{14 }\)
\(2 = \sqrt{45 - 41 }\)
\(3 = \sqrt{\frac{ 41 + 4 }{ 5 }}\)
\(4 = 45 - 41 \)
\(5 = 14 - 4 - 5 \)
\(6 = 4 \cdot 5 - 14 \)
\(7 = 51 - 44 \)
\(8 = \sqrt{15 \cdot 4 + 4 }\)
\(9 = \frac{ 41 + 4 }{ 5 }\)
\(10 = \frac{ 5! }{ \sqrt{144 } }\)
\(11 = \sqrt{145 - 4 !}\)
\(12 = \frac{ 14 }{ \sqrt{4} } + 5 \)
\(13 = 54 - 41 \)
\(14 = ( 5 - 4 ) \cdot 14 \)
\(15 = 14 - 4 + 5 \)
\(16 = \sqrt{441} - 5 \)
\(17 = \sqrt{144} + 5 \)
\(18 = \frac{ 54 }{ 4 - 1 }\)
\(19 = \sqrt{4 \cdot 4} + 15 \)
\(20 = 44 - ( 5 - 1 )!\)
\(21 = 41 - 4 \cdot 5 \)
\(22 = ( 15 - 4 ) \cdot \sqrt{4 }\)
\(23 = 14 + 4 + 5 \)
\(24 = 144 - 5 !\)
\(25 = 5^{\frac{ 4 }{ 4 } + 1 }\)
\(26 = \sqrt{441} + 5 \)
\(27 = \frac{ 54 \cdot 1 }{ \sqrt{4 } }\)
\(28 = \frac{ 54 }{ \sqrt{4} } + 1 \)
\(29 = 44 - 15 \)
\(30 = \frac{ 15 \cdot 4 }{ \sqrt{4 } }\)
\(31 = 45 - 14 \)
\(32 = 41 - 4 - 5 \)
\(33 = 14 \cdot \sqrt{4} + 5 \)
\(34 = 4 \cdot 5 + 14 \)
\(35 = 51 - 4 \cdot 4 \)
\(36 = ( 14 - 5 ) \cdot 4 \)
\(37 = ( 4 + 5 ) \cdot 4 + 1 \)
\(38 = 44 - 1 - 5 \)
\(39 = 44 \cdot 1 - 5 \)
\(40 = 54 - 14 \)
\(41 = ( 5 - 4 ) \cdot 41 \)
\(42 = 41 - 4 + 5 \)
\(43 = 44 - 1^{5 }\)
\(44 = ( 15 - 4 ) \cdot 4 \)
\(45 = 1^{5} + 44 \)
\(46 = 1^{4} + 45 \)
\(47 = 45 \cdot 1 + \sqrt{4 }\)
\(48 = 44 - 1 + 5 \)
\(49 = 44 \cdot 1 + 5 \)
\(50 = ( 14 - 4 ) \cdot 5 \)
\(51 = 14 \cdot 4 - 5 \)
\(52 = \frac{ 4 }{ 4 } + 51 \)
\(53 = 54 - 1^{4 }\)
\(54 = 1^{4} \cdot 54 \)
\(55 = 1^{4} + 54 \)
\(56 = 15 \cdot 4 - 4 \)
\(57 = 54 - 1 + 4 \)
\(58 = 54 \cdot 1 + 4 \)
\(59 = 14 + 45 \)
\(60 = \sqrt{144} \cdot 5 \)
\(61 = 14 \cdot 4 + 5 \)
\(62 = 15 \cdot 4 + \sqrt{4 }\)
\(63 = 15 + 4! + 4 !\)
\(64 = 15 \cdot 4 + 4 \)
\(65 = 4^{5 - \sqrt{4}} + 1 \)
\(66 = 14 \cdot 5 - 4 \)
\(67 = 4 \cdot 4 + 51 \)
\(68 = 14 + 54 \)
\(69 = 45 \cdot 1 + 4 !\)
\(70 = 41 + 4! + 5 \)
\(71 = \frac{ 5! }{ 4 } + 41 \)
\(72 = 14 \cdot 5 + \sqrt{4 }\)
\(73 = \sqrt{4}^{5} + 41 \)
\(74 = 14 \cdot 5 + 4 \)
\(75 = 5! - ( 41 + 4 )\)
\(76 = ( 14 + 5 ) \cdot 4 \)
\(77 = \frac{ 154 }{ \sqrt{4 } }\)
\(78 = 54 \cdot 1 + 4 !\)
\(79 = 4! \cdot 5 - 41 \)
\(80 = ( 14 + \sqrt{4} ) \cdot 5 \)
\(81 = \sqrt{14 - 5}^{4 }\)
\(82 = 5! - ( 14 + 4 ! )\)
\(83 = 5! - ( 41 - 4 )\)
\(84 = 15 \cdot 4 + 4 !\)
\(85 = ( 41 - 4! ) \cdot 5 \)
\(86 = 41 + 45 \)
\(87 = 41 \cdot \sqrt{4} + 5 \)
\(88 = \sqrt{5 - 1} \cdot 44 \)
\(89 = 45 \cdot \sqrt{4} - 1 \)
\(90 = ( 14 + 4 ) \cdot 5 \)
\(91 = 45 \cdot \sqrt{4} + 1 \)
\(92 = ( 41 + 5 ) \cdot \sqrt{4 }\)
\(93 = 5! - ( 4 - 1 + 4 ! )\)
\(94 = 14 \cdot 5 + 4 !\)
\(95 = 41 + 54 \)
\(96 = ( 1 + 5 ) \cdot 4 \cdot 4 \)
\(97 = ( 4! - 1 ) \cdot 4 + 5 \)
\(98 = ( \sqrt{4} + 5 ) \cdot 14 \)
\(99 = 5! - \sqrt{441 }\)
\(100 = ( 1 + 4 ) \cdot 4 \cdot 5 \)