All 100 targets have a solution.
\(1 = 44 - 43 \)
\(2 = 4 - ( 3 - \frac{ 4 }{ 4 } )\)
\(3 = 4 - ( 4 - 3 )^{4 }\)
\(4 = \sqrt{\frac{ 44 + 4 }{ 3 }}\)
\(5 = \frac{ 44 }{ 4 } - 3 !\)
\(6 = 34 - 4! - 4 \)
\(7 = 4 - ( 4 - 3 ) + 4 \)
\(8 = \frac{ 44 }{ 4 } - 3 \)
\(9 = \frac{ 34 + \sqrt{4} }{ 4 }\)
\(10 = 44 - 34 \)
\(11 = 3 \cdot 4 - \frac{ 4 }{ 4 }\)
\(12 = \sqrt{( 44 + 4 ) \cdot 3 }\)
\(13 = \frac{ 34 }{ \sqrt{4} } - 4 \)
\(14 = \frac{ 44 }{ 4 } + 3 \)
\(15 = \frac{ 34 - 4 }{ \sqrt{4 } }\)
\(16 = \frac{ 44 + 4 }{ 3 }\)
\(17 = \frac{ 34 \cdot \sqrt{4} }{ 4 }\)
\(18 = 34 - 4 \cdot 4 \)
\(19 = \frac{ 34 + 4 }{ \sqrt{4 } }\)
\(20 = 4^{3} - 44 \)
\(21 = \sqrt{444 - 3 }\)
\(22 = \frac{ 44 }{ 3! - 4 }\)
\(23 = 43 - 4! + 4 \)
\(24 = ( 3 + 4 ) \cdot 4 - 4 \)
\(25 = \frac{ 44 }{ \sqrt{4} } + 3 \)
\(26 = 34 - 4 - 4 \)
\(27 = 43 - 4 \cdot 4 \)
\(28 = 34 - 4 - \sqrt{4 }\)
\(29 = ( 4 + 4 ) \cdot 4 - 3 \)
\(30 = 34 - \sqrt{4 \cdot 4 }\)
\(31 = 43 - \frac{ 4! }{ \sqrt{4 } }\)
\(32 = 44 - 3 \cdot 4 \)
\(33 = 34 - \frac{ 4 }{ 4 }\)
\(34 = 34 - 4 + 4 \)
\(35 = \frac{ 4 }{ 4 } + 34 \)
\(36 = 34 - \sqrt{4} + 4 \)
\(37 = 44 - 3 - 4 \)
\(38 = \sqrt{4 \cdot 4} + 34 \)
\(39 = 43 - \sqrt{4 \cdot 4 }\)
\(40 = ( 34 - 4! ) \cdot 4 \)
\(41 = 43 - 4 + \sqrt{4 }\)
\(42 = 34 + 4 + 4 \)
\(43 = 43 - 4 + 4 \)
\(44 = \frac{ 4 }{ 4 } + 43 \)
\(45 = 44 - 3 + 4 \)
\(46 = 44 + 3! - 4 \)
\(47 = \sqrt{4 \cdot 4} + 43 \)
\(48 = 4^{3} - 4 \cdot 4 \)
\(49 = 43 + \sqrt{4} + 4 \)
\(50 = 4 \cdot 4 + 34 \)
\(51 = 43 + 4 + 4 \)
\(52 = \sqrt{4}^{3} + 44 \)
\(53 = 4 \cdot 4! - 43 \)
\(54 = 34 - 4 + 4 !\)
\(55 = \frac{ 4! }{ \sqrt{4} } + 43 \)
\(56 = 3 \cdot 4 + 44 \)
\(57 = 3^{\sqrt{4 \cdot 4}} - 4 !\)
\(58 = \sqrt{4 \cdot 4}! + 34 \)
\(59 = 4 \cdot 4 + 43 \)
\(60 = ( 34 - 4 ) \cdot \sqrt{4 }\)
\(61 = 4 \cdot 4 \cdot 4 - 3 \)
\(62 = 34 + 4 + 4 !\)
\(63 = 43 - 4 + 4 !\)
\(64 = 34 \cdot \sqrt{4} - 4 \)
\(65 = 44 - 3 + 4 !\)
\(66 = \frac{ 44 \cdot 3 }{ \sqrt{4 } }\)
\(67 = 4 \cdot 4 \cdot 4 + 3 \)
\(68 = \frac{ 34 }{ \sqrt{4} } \cdot 4 \)
\(69 = 43 + \sqrt{4} + 4 !\)
\(70 = 34 \cdot \sqrt{4} + \sqrt{4 }\)
\(71 = 43 + 4 + 4 !\)
\(72 = 34 \cdot \sqrt{4} + 4 \)
\(73 = 3^{4} - 4 - 4 \)
\(74 = \frac{ 444 }{ 3 ! }\)
\(75 = 3^{4} - 4 - \sqrt{4 }\)
\(76 = ( 34 + 4 ) \cdot \sqrt{4 }\)
\(77 = 3^{\sqrt{4 \cdot 4}} - 4 \)
\(78 = 34 + 44 \)
\(79 = 3^{4} - 4 + \sqrt{4 }\)
\(80 = 4^{3} + 4 \cdot 4 \)
\(81 = ( 4 - ( 4 - 3 ) )^{4 }\)
\(82 = 43 \cdot \sqrt{4} - 4 \)
\(83 = 3^{4} - \sqrt{4} + 4 \)
\(84 = \frac{ 4^{4} - 4 }{ 3 }\)
\(85 = 44 \cdot \sqrt{4} - 3 \)
\(86 = \frac{ 344 }{ 4 }\)
\(87 = 43 + 44 \)
\(88 = ( 3! - 4 ) \cdot 44 \)
\(89 = 3^{4} + 4 + 4 \)
\(90 = 43 \cdot \sqrt{4} + 4 \)
\(91 = 44 \cdot \sqrt{4} + 3 \)
\(92 = 34 \cdot \sqrt{4} + 4 !\)
\(93 = \sqrt{4 \cdot 4} \cdot 4! - 3 \)
\(94 = ( 43 + 4 ) \cdot \sqrt{4 }\)
\(95 = 4 \cdot 4! + 3 - 4 \)
\(96 = ( 4 + 4 ) \cdot 3 \cdot 4 \)
\(97 = 3^{4} + 4 \cdot 4 \)
\(98 = \sqrt{( 3 + 4 )^{4} \cdot 4 }\)
\(99 = \sqrt{4 \cdot 4} \cdot 4! + 3 \)
\(100 = ( 34 - 4! )^{\sqrt{4 }}\)