All 100 targets have a solution.
\(1 = ( 7 - 6 )^{25 }\)
\(2 = 7 - \sqrt{\sqrt{625 }}\)
\(3 = \frac{ 25 - 7 }{ 6 }\)
\(4 = \sqrt{72 - 56 }\)
\(5 = 62 - 57 \)
\(6 = \frac{ 56 }{ 7 } - 2 \)
\(7 = 72 - 65 \)
\(8 = 6 - \sqrt{25} + 7 \)
\(9 = \sqrt{256} - 7 \)
\(10 = 52 - 6 \cdot 7 \)
\(11 = \sqrt{\sqrt{256}} + 7 \)
\(12 = \frac{ \sqrt{576} }{ 2 }\)
\(13 = 75 - 62 \)
\(14 = 26 - 5 - 7 \)
\(15 = 67 - 52 \)
\(16 = 72 - 56 \)
\(17 = 6 \cdot 7 - 25 \)
\(18 = \sqrt{625} - 7 \)
\(19 = \frac{ 57 \cdot 2 }{ 6 }\)
\(20 = 2 + 5 + 6 + 7 \)
\(21 = \frac{ 56 }{ 2 } - 7 \)
\(22 = \sqrt{576} - 2 \)
\(23 = \sqrt{256} + 7 \)
\(24 = 76 - 52 \)
\(25 = ( 7 - 6 ) \cdot 25 \)
\(26 = \sqrt{576} + 2 \)
\(27 = ( 6 - 5 ) \cdot 27 \)
\(28 = 26 - 5 + 7 \)
\(29 = 56 - 27 \)
\(30 = \sqrt{75 \cdot 2 \cdot 6 }\)
\(31 = 57 - 26 \)
\(32 = \sqrt{625} + 7 \)
\(33 = \frac{ 76 }{ 2 } - 5 \)
\(34 = 6^{2} + 5 - 7 \)
\(35 = \frac{ 56 }{ 2 } + 7 \)
\(36 = \frac{ 65 + 7 }{ 2 }\)
\(37 = \sqrt{25} \cdot 6 + 7 \)
\(38 = 65 - 27 \)
\(39 = 52 - 6 - 7 \)
\(40 = \frac{ 6! }{ 25 - 7 }\)
\(41 = \sqrt{25} \cdot 7 + 6 \)
\(42 = 67 - 25 \)
\(43 = \frac{ 76 }{ 2 } + 5 \)
\(44 = 76 - 2^{5 }\)
\(45 = 57 - 2 \cdot 6 \)
\(46 = 5! - ( 76 - 2 )\)
\(47 = 56 - 2 - 7 \)
\(48 = \sqrt{576} \cdot 2 \)
\(49 = 75 - 26 \)
\(50 = 62 - 5 - 7 \)
\(51 = 76 - 25 \)
\(52 = ( 7 - 5 ) \cdot 26 \)
\(53 = 52 - 6 + 7 \)
\(54 = 57 - \frac{ 6 }{ 2 }\)
\(55 = 57 - \sqrt{6 - 2 }\)
\(56 = 65 - 2 - 7 \)
\(57 = 5 \cdot 6 + 27 \)
\(58 = \sqrt{65^{2}} - 7 \)
\(59 = \sqrt{2 + 7} + 56 \)
\(60 = \frac{ 6 }{ 2 } + 57 \)
\(61 = 5 \cdot 7 + 26 \)
\(62 = 67 - \sqrt{25 }\)
\(63 = 2^{7} - 65 \)
\(64 = ( \frac{ 56 }{ 7 } )^{2 }\)
\(65 = 52 + 6 + 7 \)
\(66 = 76 - 2 \cdot 5 \)
\(67 = 6 \cdot 7 + 25 \)
\(68 = \sqrt{2 + 7} + 65 \)
\(69 = 2 \cdot 6 + 57 \)
\(70 = 2 \cdot 7 + 56 \)
\(71 = 76 - \sqrt{25 }\)
\(72 = \sqrt{25} + 67 \)
\(73 = 72 - 5 + 6 \)
\(74 = 62 + 5 + 7 \)
\(75 = ( 2 + 6 + 7 ) \cdot 5 \)
\(76 = 2^{6} + 5 + 7 \)
\(77 = 2 \cdot 5 + 67 \)
\(78 = \frac{ 6 }{ 2 } + 75 \)
\(79 = 2 \cdot 7 + 65 \)
\(80 = \frac{ 7! }{ 65 - 2 }\)
\(81 = \sqrt{25} + 76 \)
\(82 = 5! - \frac{ 76 }{ 2 }\)
\(83 = 26 + 57 \)
\(84 = ( 2 + 5 + 7 ) \cdot 6 \)
\(85 = ( ( 6 - 2 )! - 7 ) \cdot 5 \)
\(86 = 2 \cdot 5 + 76 \)
\(87 = 2 \cdot 6 + 75 \)
\(88 = \frac{ 7! }{ 56 } - 2 \)
\(89 = 2 \cdot 6 \cdot 7 + 5 \)
\(90 = \frac{ 7! }{ \sqrt{56^{2 }} }\)
\(91 = ( 2 + 5 + 6 ) \cdot 7 \)
\(92 = 25 + 67 \)
\(93 = 6^{2} + 57 \)
\(94 = 6 \cdot 7 + 52 \)
\(95 = ( 26 - 7 ) \cdot 5 \)
\(96 = ( 2 + 6 ) \cdot ( 5 + 7 )\)
\(97 = 5 \cdot 7 + 62 \)
\(98 = ( 56 - 7 ) \cdot 2 \)
\(99 = 2^{5} + 67 \)
\(100 = ( 2 \cdot 7 + 6 ) \cdot 5 \)