99 of 100 targets have a solution.
\(1 = \frac{ 47 }{ 47 }\)
\(2 = 7^{\sqrt{4}} - 47 \)
\(3 = 4 - 4^{7 - 7 }\)
\(4 = ( 7 - 7 ) \cdot 4 + 4 \)
\(5 = 7 \cdot 7 - 44 \)
\(6 = \sqrt{47 - 4 - 7 }\)
\(7 = \frac{ 47 + \sqrt{4} }{ 7 }\)
\(8 = 7^{4 - 4} + 7 \)
\(9 = \frac{ 7 }{ 7 } + 4 + 4 \)
\(10 = \frac{ 47 - 7 }{ 4 }\)
\(11 = \sqrt{44 + 77 }\)
\(12 = ( 4 - \frac{ 7 }{ 7 } ) \cdot 4 \)
\(13 = \sqrt{74 + 7} + 4 \)
\(14 = \frac{ 74 + 4! }{ 7 }\)
\(15 = \frac{ 4 }{ 4 } + 7 + 7 \)
\(16 = 47 - 4! - 7 \)
\(17 = \sqrt{74 \cdot 4 - 7 }\)
\(18 = \sqrt{( 74 + 7 ) \cdot 4 }\)
\(19 = 47 - 4 \cdot 7 \)
\(20 = \frac{ 47 - 7 }{ \sqrt{4 } }\)
\(21 = ( 7 - \sqrt{4 \cdot 4} ) \cdot 7 \)
\(22 = 4 + 4 + 7 + 7 \)
\(23 = 4 \cdot 7 + \sqrt{4} - 7 \)
\(24 = ( ( 7 - 7 ) \cdot 4 + 4 )!\)
\(25 = 74 - 7^{\sqrt{4 }}\)
\(26 = \sqrt{\frac{ 7! }{ 7 } - 44 }\)
\(27 = 74 - 47 \)
\(28 = \frac{ 4 + 4! }{ 7 } \cdot 7 \)
\(29 = 77 - 4! - 4 !\)
\(30 = 44 - 7 - 7 \)
\(31 = 4 \cdot 7 - 4 + 7 \)
\(32 = \sqrt{4}^{\frac{ 7 }{ 7 } + 4 }\)
\(33 = 77 - 44 \)
\(34 = 4! - 4 + 7 + 7 \)
\(35 = ( 7 - ( 4 - \sqrt{4} ) ) \cdot 7 \)
\(36 = 47 - 4 - 7 \)
\(37 = 44 - \sqrt{7 \cdot 7 }\)
\(38 = 47 - \sqrt{4} - 7 \)
\(39 = 4 \cdot 7 + 4 + 7 \)
\(40 = ( 7 - 4 + 7 ) \cdot 4 \)
\(41 = 47 - ( 7 - 4 )!\)
\(42 = 47 + \sqrt{4} - 7 \)
\(43 = 44 - \frac{ 7 }{ 7 }\)
\(44 = 44 - 7 + 7 \)
\(45 = \frac{ 7 }{ 7 } + 44 \)
\(46 = 74 - 4 \cdot 7 \)
\(47 = \sqrt{47 \cdot 47 }\)
\(48 = 7 \cdot 7 - \frac{ 4 }{ 4 }\)
\(49 = 77 - 4! - 4 \)
\(50 = 47 - 4 + 7 \)
\(51 = \sqrt{7 \cdot 7} + 44 \)
\(52 = 47 - \sqrt{4} + 7 \)
\(53 = ( 7 - 4 )! + 47 \)
\(54 = \sqrt{4}^{7} - 74 \)
\(55 = 77 - 4! + \sqrt{4 }\)
\(56 = 47 + \sqrt{4} + 7 \)
\(57 = 74 - 4! + 7 \)
\(58 = 44 + 7 + 7 \)
\(59 = 4 \cdot 7 + 4! + 7 \)
\(60 = 74 - \sqrt{4} \cdot 7 \)
\(61 = 77 - 4 \cdot 4 \)
\(62 = \sqrt{4} \cdot 4! + 7 + 7 \)
\(63 = 74 - 4 - 7 \)
\(64 = 47 + 4! - 7 \)
\(65 = 74 - \sqrt{4} - 7 \)
\(66 = ( 7 - 4 )! \cdot ( 4 + 7 )\)
\(67 = \sqrt{74^{\sqrt{4}}} - 7 \)
\(68 = 74 - ( 7 - 4 )!\)
\(69 = 77 - 4 - 4 \)
\(70 = \frac{ 7! }{ 74 - \sqrt{4 } }\)
\(71 = 74 + 4 - 7 \)
\(72 = \frac{ 7! }{ 74 - 4 }\)
\(73 = 77 - \sqrt{4 \cdot 4 }\)
\(74 = \sqrt{74 \cdot 74 }\)
\(75 = 4 \cdot 7 + 47 \)
\(76 = 77 - \frac{ 4 }{ 4 }\)
\(77 = 74 - 4 + 7 \)
\(78 = \frac{ 4 }{ 4 } + 77 \)
\(79 = 74 - \sqrt{4} + 7 \)
\(80 = ( 47 - 7 ) \cdot \sqrt{4 }\)
\(81 = \sqrt{4}^{7} - 47 \)
\(82 = 4 \cdot 4! - 7 - 7 \)
\(83 = 74 + \sqrt{4} + 7 \)
\(84 = ( 7 - 4 ) \cdot 4 \cdot 7 \)
\(85 = 74 + 4 + 7 \)
\(86 = ?\)
\(87 = 47 \cdot \sqrt{4} - 7 \)
\(88 = \sqrt{7744 }\)
\(89 = \frac{ 4! }{ \sqrt{4} } + 77 \)
\(90 = \frac{ 7! }{ ( 4 + 4 ) \cdot 7 }\)
\(91 = 74 + 4! - 7 \)
\(92 = ( 4! - \frac{ 7 }{ 7 } ) \cdot 4 \)
\(93 = 7 \cdot 7 + 44 \)
\(94 = 47 + 47 \)
\(95 = 4 \cdot 4! - \frac{ 7 }{ 7 }\)
\(96 = 7^{\sqrt{4}} + 47 \)
\(97 = 77 - 4 + 4 !\)
\(98 = ( 4 - \sqrt{4} ) \cdot 7 \cdot 7 \)
\(99 = 77 - \sqrt{4} + 4 !\)
\(100 = ( 7 - 4 + 7 )^{\sqrt{4 }}\)