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