All 100 targets have a solution.
\(1 = 47^{4 - 4 }\)
\(2 = \sqrt{\frac{ 44 }{ 4 } - 7 }\)
\(3 = 47 - 44 \)
\(4 = \frac{ 44 }{ 4 } - 7 \)
\(5 = 7^{\sqrt{4}} - 44 \)
\(6 = ( 47 - 44 )!\)
\(7 = ( 4 - 4 ) \cdot 4 + 7 \)
\(8 = 4^{4 - 4} + 7 \)
\(9 = \frac{ 4 + 4 }{ 4 } + 7 \)
\(10 = 4 - \frac{ 4 }{ 4 } + 7 \)
\(11 = 4 - 4 + 4 + 7 \)
\(12 = \frac{ 4 }{ 4 } + 4 + 7 \)
\(13 = 44 - 4! - 7 \)
\(14 = \frac{ 4 + 4 }{ 4 } \cdot 7 \)
\(15 = \frac{ 44 }{ \sqrt{4} } - 7 \)
\(16 = 44 - 4 \cdot 7 \)
\(17 = ( 4 - 4 + 4 )! - 7 \)
\(18 = \frac{ 44 }{ 4 } + 7 \)
\(19 = 47 - 4! - 4 \)
\(20 = 4 \cdot 7 - 4 - 4 \)
\(21 = ( 4 - \frac{ 4 }{ 4 } ) \cdot 7 \)
\(22 = \sqrt{( 4 + 7 ) \cdot 44 }\)
\(23 = 47 - \sqrt{4 \cdot 4 }!\)
\(24 = ( \frac{ 44 }{ 4 } - 7 )!\)
\(25 = ( 4 + 4 ) \cdot 4 - 7 \)
\(26 = 74 - 4! - 4 !\)
\(27 = 44 - 4! + 7 \)
\(28 = ( 4 - 4 + 4 ) \cdot 7 \)
\(29 = \frac{ 44 }{ \sqrt{4} } + 7 \)
\(30 = 74 - 44 \)
\(31 = \frac{ 744 }{ 4 ! }\)
\(32 = ( \frac{ 4 }{ 4 } + 7 ) \cdot 4 \)
\(33 = 44 - 4 - 7 \)
\(34 = 4 \cdot 7 + \sqrt{4} + 4 \)
\(35 = 44 - \sqrt{4} - 7 \)
\(36 = \frac{ 4^{4} - 4 }{ 7 }\)
\(37 = \frac{ 74 \cdot \sqrt{4} }{ 4 }\)
\(38 = 44 - ( 7 - 4 )!\)
\(39 = 47 - 4 - 4 \)
\(40 = ( 4 + 7 ) \cdot 4 - 4 \)
\(41 = 44 + 4 - 7 \)
\(42 = ( 4 - \frac{ 4 }{ 4 } )! \cdot 7 \)
\(43 = 47 - \sqrt{4 \cdot 4 }\)
\(44 = 4 \cdot 4 + 4 \cdot 7 \)
\(45 = 47 - 4 + \sqrt{4 }\)
\(46 = 47 - \frac{ 4 }{ 4 }\)
\(47 = 44 - 4 + 7 \)
\(48 = \frac{ 4 }{ 4 } + 47 \)
\(49 = 44 - \sqrt{4} + 7 \)
\(50 = ( 7 - 4 )! + 44 \)
\(51 = \sqrt{4 \cdot 4} + 47 \)
\(52 = ( 4 + 4 ) \cdot 7 - 4 \)
\(53 = 44 + \sqrt{4} + 7 \)
\(54 = 74 - 4! + 4 \)
\(55 = 44 + 4 + 7 \)
\(56 = ( 4 - \sqrt{4} ) \cdot 4 \cdot 7 \)
\(57 = 4 \cdot 4 \cdot 4 - 7 \)
\(58 = 74 - 4 \cdot 4 \)
\(59 = \frac{ 4! }{ \sqrt{4} } + 47 \)
\(60 = ( 4 + 4 + 7 ) \cdot 4 \)
\(61 = 44 + 4! - 7 \)
\(62 = 74 - \frac{ 4! }{ \sqrt{4 } }\)
\(63 = 4 \cdot 4 + 47 \)
\(64 = \frac{ 4^{7} }{ 4^{4 } }\)
\(65 = 4 \cdot 4 + 7^{\sqrt{4 }}\)
\(66 = 74 - 4 - 4 \)
\(67 = 47 - 4 + 4 !\)
\(68 = 74 - 4 - \sqrt{4 }\)
\(69 = 47 - \sqrt{4} + 4 !\)
\(70 = 74 - \sqrt{4 \cdot 4 }\)
\(71 = 4 \cdot 4 \cdot 4 + 7 \)
\(72 = 4 \cdot 7 + 44 \)
\(73 = 74 - \frac{ 4 }{ 4 }\)
\(74 = 74 - 4 + 4 \)
\(75 = \frac{ 4 }{ 4 } + 74 \)
\(76 = 74 - \sqrt{4} + 4 \)
\(77 = \frac{ 44 }{ 4 } \cdot 7 \)
\(78 = \sqrt{4 \cdot 4} + 74 \)
\(79 = ( 7 - 4 )^{4} - \sqrt{4 }\)
\(80 = 74 + \sqrt{4} + 4 \)
\(81 = 44 \cdot \sqrt{4} - 7 \)
\(82 = 74 + 4 + 4 \)
\(83 = ( 7 - 4 )^{4} + \sqrt{4 }\)
\(84 = \sqrt{4}^{7} - 44 \)
\(85 = ( 7 - 4 )^{4} + 4 \)
\(86 = ( 47 - 4 ) \cdot \sqrt{4 }\)
\(87 = ( 4! - 4 ) \cdot 4 + 7 \)
\(88 = ( 4 + 4 ) \cdot ( 4 + 7 )\)
\(89 = \sqrt{4 \cdot 4} \cdot 4! - 7 \)
\(90 = 4 \cdot 4 + 74 \)
\(91 = 44 + 47 \)
\(92 = ( 47 - 4! ) \cdot 4 \)
\(93 = 7^{\sqrt{4}} + 44 \)
\(94 = \frac{ 47 \cdot 4 }{ \sqrt{4 } }\)
\(95 = 44 \cdot \sqrt{4} + 7 \)
\(96 = ( 4 \cdot 7 - 4 ) \cdot 4 \)
\(97 = ( \sqrt{4} + 4! ) \cdot 4 - 7 \)
\(98 = 47 \cdot \sqrt{4} + 4 \)
\(99 = 4 \cdot 4! - 4 + 7 \)
\(100 = ( 74 - 4! ) \cdot \sqrt{4 }\)