All 100 targets have a solution.
\(1 = ( 278 \cdot 0 )!\)
\(2 = 78 \cdot 0 + 2 \)
\(3 = 78^{0} + 2 \)
\(4 = \frac{ 20 + 8 }{ 7 }\)
\(5 = 20 - 7 - 8 \)
\(6 = 7 - 28^{0 }\)
\(7 = 8 - 27^{0 }\)
\(8 = 80 - 72 \)
\(9 = 27^{0} + 8 \)
\(10 = \frac{ 72 }{ 8 } + 0 !\)
\(11 = 7^{0} + 2 + 8 \)
\(12 = 82 - 70 \)
\(13 = 7 - ( 0 + 2 ) + 8 \)
\(14 = \sqrt{( 20 + 8 ) \cdot 7 }\)
\(15 = 0 \cdot 2 + 7 + 8 \)
\(16 = \frac{ 80 }{ 7 - 2 }\)
\(17 = 0 + 2 + 7 + 8 \)
\(18 = \frac{ 7! }{ 280 }\)
\(19 = 20 + 7 - 8 \)
\(20 = ( 8 - 7 ) \cdot 20 \)
\(21 = 20 - 7 + 8 \)
\(22 = 28 + 0! - 7 \)
\(23 = ( 0 + 2 ) \cdot 8 + 7 \)
\(24 = ( \frac{ 20 + 8 }{ 7 } )!\)
\(25 = ( \frac{ 28 }{ 7 } )! + 0 !\)
\(26 = 27 - 8^{0 }\)
\(27 = 0 \cdot 8 + 27 \)
\(28 = 8^{0} + 27 \)
\(29 = 7^{0} + 28 \)
\(30 = ( 0 + 7 + 8 ) \cdot 2 \)
\(31 = \frac{ 70 - 8 }{ 2 }\)
\(32 = ( 7 - ( 0! + 2 ) ) \cdot 8 \)
\(33 = \frac{ 80 }{ 2 } - 7 \)
\(34 = 27 - 0! + 8 \)
\(35 = 20 + 7 + 8 \)
\(36 = 7 \cdot 8 - 20 \)
\(37 = \sqrt{\sqrt{\sqrt{2 + 7}!^{8}}} + 0 !\)
\(38 = \frac{ 78 }{ 2 } - 0 !\)
\(39 = \frac{ 70 + 8 }{ 2 }\)
\(40 = \frac{ 280 }{ 7 }\)
\(41 = 7^{0 + 2} - 8 \)
\(42 = 70 - 28 \)
\(43 = \frac{ 70 }{ 2 } + 8 \)
\(44 = \frac{ 87 + 0! }{ 2 }\)
\(45 = ( 0! + 2 ) \cdot ( 7 + 8 )\)
\(46 = 70 - ( \frac{ 8 }{ 2 } )!\)
\(47 = \frac{ 80 }{ 2 } + 7 \)
\(48 = 2^{7} - 80 \)
\(49 = 7^{0 \cdot 8 + 2 }\)
\(50 = 8^{0} + 7^{2 }\)
\(51 = ( 8 - 0! ) \cdot 7 + 2 \)
\(52 = \sqrt{0! + 8} + 7^{2 }\)
\(53 = 80 - 27 \)
\(54 = 70 - 2 \cdot 8 \)
\(55 = 7 \cdot 8 - 2^{0 }\)
\(56 = \frac{ 8! }{ 720 }\)
\(57 = 7^{0 + 2} + 8 \)
\(58 = 78 - 20 \)
\(59 = 7 \cdot 8 + 0! + 2 \)
\(60 = 70 - 2 - 8 \)
\(61 = \frac{ 7! }{ 80 } - 2 \)
\(62 = \sqrt{70^{2}} - 8 \)
\(63 = 72 - 0! - 8 \)
\(64 = 70 + 2 - 8 \)
\(65 = 72 + 0! - 8 \)
\(66 = 70 - \frac{ 8 }{ 2 }\)
\(67 = 87 - 20 \)
\(68 = 70 - \sqrt{\frac{ 8 }{ 2 }}\)
\(69 = \sqrt{\sqrt{7^{8}}} + 20 \)
\(70 = ( 0 + 2 + 8 ) \cdot 7 \)
\(71 = 72 - 8^{0 }\)
\(72 = 0 \cdot 8 + 72 \)
\(73 = 8^{0} + 72 \)
\(74 = \frac{ 8 }{ 2 } + 70 \)
\(75 = 80 + 2 - 7 \)
\(76 = 7 \cdot 8 + 20 \)
\(77 = 78 - 2^{0 }\)
\(78 = 0 \cdot 2 + 78 \)
\(79 = 2^{0} + 78 \)
\(80 = 70 + 2 + 8 \)
\(81 = 82 - 7^{0 }\)
\(82 = 0 \cdot 7 + 82 \)
\(83 = 7^{0} + 82 \)
\(84 = ( 20 - 8 ) \cdot 7 \)
\(85 = 80 - 2 + 7 \)
\(86 = 2 \cdot 8 + 70 \)
\(87 = 0 \cdot 2 + 87 \)
\(88 = 2^{0} + 87 \)
\(89 = 80 + 2 + 7 \)
\(90 = \frac{ 720 }{ 8 }\)
\(91 = \frac{ \sqrt{2 + 7}!! }{ 8 } + 0 !\)
\(92 = \frac{ ( 7 - 0! )! }{ 8 } + 2 \)
\(93 = ( 0! + 2 )! + 87 \)
\(94 = 2 \cdot 7 + 80 \)
\(95 = \sqrt{0! + 7!} + ( \frac{ 8 }{ 2 } )!\)
\(96 = ( 7 - 0! ) \cdot 2 \cdot 8 \)
\(97 = \frac{ ( 0! + 2 )!! }{ 8 } + 7 \)
\(98 = 20 + 78 \)
\(99 = \sqrt{0! + 7!} + 28 \)
\(100 = \sqrt{2 \cdot 7! - 80 }\)