All 100 targets have a solution.
\(1 = 14 - 6 - 7 \)
\(2 = \sqrt{6 - \frac{ 14 }{ 7 }}\)
\(3 = \frac{ 6 }{ \frac{ 14 }{ 7 } }\)
\(4 = 6 - \frac{ 14 }{ 7 }\)
\(5 = \sqrt{71 - 46 }\)
\(6 = 6! - 714 \)
\(7 = 71 - 64 \)
\(8 = \frac{ 14 }{ 7 } + 6 \)
\(9 = \sqrt{14 + 67 }\)
\(10 = 16 - ( 7 - 4 )!\)
\(11 = \frac{ 16 }{ 4 } + 7 \)
\(12 = \frac{ 14 \cdot 6 }{ 7 }\)
\(13 = 74 - 61 \)
\(14 = 61 - 47 \)
\(15 = 14 - 6 + 7 \)
\(16 = \sqrt{64} + 1 + 7 \)
\(17 = \frac{ 61 + 7 }{ 4 }\)
\(18 = \frac{ 76 }{ 4 } - 1 \)
\(19 = 16 - 4 + 7 \)
\(20 = \frac{ 76 }{ 4 } + 1 \)
\(21 = 741 - 6 !\)
\(22 = ( 7 - 4 )! + 16 \)
\(23 = 47 - \sqrt{16 }!\)
\(24 = ( 6 - \frac{ 14 }{ 7 } )!\)
\(25 = 71 - 46 \)
\(26 = 67 - 41 \)
\(27 = 14 + 6 + 7 \)
\(28 = 6 \cdot 7 - 14 \)
\(29 = \frac{ 174 }{ 6 }\)
\(30 = \sqrt{4} \cdot 7 + 16 \)
\(31 = 47 - 16 \)
\(32 = \sqrt{16} \cdot 7 + 4 \)
\(33 = 61 - 4 \cdot 7 \)
\(34 = ( 6 - 4 ) \cdot 17 \)
\(35 = 76 - 41 \)
\(36 = 6^{\frac{ 14 }{ 7 }}\)
\(37 = \frac{ 74 }{ \sqrt{\sqrt{16 }} }\)
\(38 = 46 - 1 - 7 \)
\(39 = 46 \cdot 1 - 7 \)
\(40 = 41 + 6 - 7 \)
\(41 = 4 \cdot 6 + 17 \)
\(42 = \sqrt{1764 }\)
\(43 = 47 - \sqrt{16 }\)
\(44 = \frac{ 176 }{ 4 }\)
\(45 = 46 - 1^{7 }\)
\(46 = 1^{7} \cdot 46 \)
\(47 = 64 - 17 \)
\(48 = ( 7 - 4 ) \cdot 16 \)
\(49 = \sqrt{\sqrt{16}} + 47 \)
\(50 = 61 - 4 - 7 \)
\(51 = \sqrt{16} + 47 \)
\(52 = 46 - 1 + 7 \)
\(53 = 67 - 14 \)
\(54 = 41 + 6 + 7 \)
\(55 = 61 - ( 7 - 4 )!\)
\(56 = ( 14 - 6 ) \cdot 7 \)
\(57 = 16 \cdot 4 - 7 \)
\(58 = 74 - 16 \)
\(59 = 71 - \sqrt{4} \cdot 6 \)
\(60 = \frac{ 7! }{ 14 \cdot 6 }\)
\(61 = 71 - 4 - 6 \)
\(62 = 76 - 14 \)
\(63 = 16 + 47 \)
\(64 = ( \frac{ 14 }{ 7 } )^{6 }\)
\(65 = 1^{7} + 64 \)
\(66 = 67 - 1^{4 }\)
\(67 = 1^{4} \cdot 67 \)
\(68 = \sqrt{7! - 416 }\)
\(69 = \sqrt{4761 }\)
\(70 = 74 - \sqrt{16 }\)
\(71 = 16 \cdot 4 + 7 \)
\(72 = 61 + 4 + 7 \)
\(73 = 71 - 4 + 6 \)
\(74 = 17 \cdot 4 + 6 \)
\(75 = 1^{6} + 74 \)
\(76 = 1^{4} \cdot 76 \)
\(77 = 14 \cdot 6 - 7 \)
\(78 = \sqrt{16} + 74 \)
\(79 = \sqrt{64} + 71 \)
\(80 = 74 \cdot 1 + 6 \)
\(81 = 14 + 67 \)
\(82 = ( 4 - 1 )! + 76 \)
\(83 = 6 \cdot 7 + 41 \)
\(84 = ( 16 - 4 ) \cdot 7 \)
\(85 = \sqrt{4} \cdot 6 \cdot 7 + 1 \)
\(86 = ( 6 \cdot 7 + 1 ) \cdot \sqrt{4 }\)
\(87 = \frac{ 6! - 4! }{ 1 + 7 }\)
\(88 = \frac{ 176 }{ \sqrt{4 } }\)
\(89 = 4 \cdot 7 + 61 \)
\(90 = 14 + 76 \)
\(91 = 14 \cdot 6 + 7 \)
\(92 = 14 \cdot 7 - 6 \)
\(93 = \frac{ 4! + 6! }{ 1 + 7 }\)
\(94 = \sqrt{\sqrt{16}} \cdot 47 \)
\(95 = 4 \cdot 6 + 71 \)
\(96 = ( 7 - 4 )! \cdot 16 \)
\(97 = \frac{ 6! - 41 }{ 7 }\)
\(98 = 17 \cdot 6 - 4 \)
\(99 = 76 - 1 + 4 !\)
\(100 = 17 \cdot 6 - \sqrt{4 }\)