4つの4(ver.1)


時事ネタ.(もう流行りは過ぎた.)
なるしす さんの4つの4で1~100を作ろう(以下URL)が流行っている.よって便乗した.の2回目.
http://www.nicovideo.jp/watch/sm27096518

・使える2項演算子は次のようにした.
\(x+y\)
\(x-y\)
\(x\times y\)
\(\frac{x}{y}\)

・使える1項演算子は次のようにした.
\(x!\)(ただし、\(x=3,4\)の場合に限る)
\(\sqrt{x}\)(ただし、\(x>0\)の場合に限る)

また、1項演算子の連続した使用はなしとする.

・4を使用した定数として次のものが使える.
\(44,444,4444\) (4を並べて使う)
\(.4\)(小数点を省略)
\(.\dot{4}\)(循環小数)\((=\frac{4}{9})\)

さらに、計算機の性能の制限が次のようにあるとする.
計算過程において,\(1000000\)を超えた場合、これを捨てる.

以上の条件で可能な正の整数は次の通りである(これ以外にはない).
\[ 0 = \left(\left(\sqrt{.4}-4!\right)+4!\right)-\sqrt{.4} \]
\[ 1 = \frac{4}{\left(.4\times.4\right)}-4! \]
\[ 2 = \frac{\left(\sqrt{4}+.4\right)}{.4}-4 \]
\[ 3 = \sqrt{\left(\frac{\sqrt{.\dot{4}}}{\left(.4-.\dot{4}\right)}+4!\right)} \]
\[ 4 = \sqrt{\left(4!\times\sqrt{\left(\left(.\dot{4}+4!\right)-4!\right)}\right)} \]
\[ 5 = \frac{\sqrt{\frac{4}{\sqrt{.4}}}}{\sqrt{\left(.4\times\sqrt{.4}\right)}} \]
\[ 6 = \frac{\frac{4}{\sqrt{.4}}}{\sqrt{.4}}-4 \]
\[ 7 = \frac{\left(\left(.4+.4\right)+\sqrt{4}\right)}{.4} \]
\[ 8 = \sqrt{\frac{\left(.\dot{4}-.4\right)}{.4}}\times4! \]
\[ 9 = \frac{\sqrt{.\dot{4}}}{\left(.4-.\dot{4}\right)}+4! \]
\[ 10 = \frac{.4}{\left(.4\times.4\right)}\times4 \]
\[ 11 = \frac{44}{\sqrt{\left(4\times4\right)}} \]
\[ 12 = \frac{\left(\left(.4+.4\right)+4\right)}{.4} \]
\[ 13 = 4!-\frac{44}{4} \]
\[ 14 = 4!+\frac{.\dot{4}}{\left(.4-.\dot{4}\right)} \]
\[ 15 = \frac{.4}{\left(.4-.\dot{4}\right)}+4! \]
\[ 16 = 4!\times\sqrt{\left(\left(.\dot{4}+4!\right)-4!\right)} \]
\[ 17 = \frac{\left(4!+44\right)}{4} \]
\[ 18 = \frac{\frac{4!}{\left(4-\sqrt{.\dot{4}}\right)}}{.4} \]
\[ 19 = \frac{\left(\left(4-.4\right)+4\right)}{.4} \]
\[ 20 = .\dot{4}+\left(44\times.\dot{4}\right) \]
\[ 21 = \frac{4}{\left(.4\times.4\right)}-4 \]
\[ 22 = \left(\left(4!-\sqrt{.\dot{4}}\right)-\sqrt{.\dot{4}}\right)-\sqrt{.\dot{4}} \]
\[ 23 = \frac{4}{\left(.4\times.4\right)}-\sqrt{4} \]
\[ 24 = \frac{\left(\frac{4}{.4}-.4\right)}{.4} \]
\[ 25 = \frac{\frac{4}{\sqrt{.4}}}{\left(.4\times\sqrt{.4}\right)} \]
\[ 26 = \frac{4!}{\frac{.4}{.\dot{4}}}-\sqrt{.\dot{4}} \]
\[ 27 = \frac{4}{\left(.4\times.4\right)}+\sqrt{4} \]
\[ 28 = \frac{\left(\left(4+4!\right)\times.\dot{4}\right)}{.\dot{4}} \]
\[ 29 = \frac{4}{\left(.4\times.4\right)}+4 \]
\[ 30 = \frac{\left(\left(4+4\right)+4\right)}{.4} \]
\[ 31 = 4!+\frac{\left(4+4!\right)}{4} \]
\[ 32 = \sqrt{\left(4!\times.\dot{4}\right)}\times\sqrt{\left(4!\times4\right)} \]
\[ 33 = \frac{44}{\sqrt{\left(.\dot{4}\times4\right)}} \]
\[ 34 = 44-\frac{4}{.4} \]
\[ 35 = \frac{44}{4}+4! \]
\[ 36 = \frac{\left(4!-\left(.4\times4!\right)\right)}{.4} \]
\[ 37 = \frac{\left(.4+4!\right)}{.4}-4! \]
\[ 38 = \frac{4!}{\frac{.4}{\sqrt{.\dot{4}}}}-\sqrt{4} \]
\[ 39 = 44-\frac{\sqrt{4}}{.4} \]
\[ 40 = \frac{\frac{4}{\sqrt{.4}}}{\sqrt{.4}}\times4 \]
\[ 41 = \frac{\left(.4+\left(4\times4\right)\right)}{.4} \]
\[ 42 = \frac{4!}{\frac{.4}{\sqrt{.\dot{4}}}}+\sqrt{4} \]
\[ 43 = 44-\frac{4}{4} \]
\[ 44 = \frac{.4}{\frac{.4}{44}} \]
\[ 45 = 44+\frac{4}{4} \]
\[ 46 = \left(44+4\right)-\sqrt{4} \]
\[ 47 = \sqrt{\frac{4}{.\dot{4}}}+44 \]
\[ 48 = \frac{\sqrt{4}}{\sqrt{.4}}\times\left(\sqrt{.4}\times4!\right) \]
\[ 49 = \frac{\sqrt{4}}{.4}+44 \]
\[ 50 = \frac{\left(4+4\right)}{\left(.4\times.4\right)} \]
\[ 51 = \frac{\left(\left(.4-4\right)+4!\right)}{.4} \]
\[ 52 = \left(44+4\right)+4 \]
\[ 53 = \frac{4}{.\dot{4}}+44 \]
\[ 54 = \frac{4!}{\left(.\dot{4}\times\sqrt{.4}\right)}\times\sqrt{.4} \]
\[ 55 = \frac{44}{\left(.4+.4\right)} \]
\[ 56 = \frac{\left(4!-\left(.4\times4\right)\right)}{.4} \]
\[ 57 = \frac{\left(.4+4!\right)}{.4}-4 \]
\[ 58 = \frac{\left(4!-\left(.4+.4\right)\right)}{.4} \]
\[ 59 = \frac{\left(.4+4!\right)}{.4}-\sqrt{4} \]
\[ 60 = 4!\times\frac{.4}{\left(.4\times.4\right)} \]
\[ 61 = \frac{\left(.4+4!\right)}{\sqrt{\left(.4\times.4\right)}} \]
\[ 62 = \frac{\left(.4+\left(.4+4!\right)\right)}{.4} \]
\[ 63 = \frac{\left(.4+4!\right)}{.4}+\sqrt{4} \]
\[ 64 = \frac{4!}{\frac{.4}{\sqrt{.\dot{4}}}}+4! \]
\[ 65 = 4+\frac{\left(.4+4!\right)}{.4} \]
\[ 66 = \frac{\left(\left(\sqrt{4}+.4\right)+4!\right)}{.4} \]
\[ 67 = \frac{\left(4+4!\right)}{.\dot{4}}+4 \]
\[ 68 = 4+\left(\left(4\times4\right)\times4\right) \]
\[ 69 = \frac{\left(44+\sqrt{4}\right)}{\sqrt{.\dot{4}}} \]
\[ 70 = \sqrt{4}+\left(4!+44\right) \]
\[ 71 = \frac{\left(\left(4+4!\right)+.4\right)}{.4} \]
\[ 72 = \frac{\left(4!\times\sqrt{\left(4-.4\right)}\right)}{\sqrt{.4}} \]
\[ 73 = \frac{\left(\sqrt{.\dot{4}}+\left(4!\times\sqrt{4}\right)\right)}{\sqrt{.\dot{4}}} \]
\[ 74 = 4+\frac{\left(4+4!\right)}{.4} \]
\[ 75 = \frac{4!}{\left(.4\times\left(.4+.4\right)\right)} \]
\[ 76 = \left(\left(4!-4\right)\times4\right)-4 \]
\[ 77 = \frac{\left(4!-.\dot{4}\right)}{.\dot{4}}+4! \]
\[ 78 = \left(\left(4!-4\right)\times4\right)-\sqrt{4} \]
\[ 79 = \frac{\left(4!-\sqrt{4}\right)}{.4}+4! \]
\[ 80 = \sqrt{4}\times\frac{4!}{\frac{.4}{\sqrt{.\dot{4}}}} \]
\[ 81 = \frac{\frac{4}{.\dot{4}}}{\frac{.\dot{4}}{4}} \]
\[ 82 = \left(\left(4!-4\right)\times4\right)+\sqrt{4} \]
\[ 83 = 4!-\frac{\left(.4-4!\right)}{.4} \]
\[ 84 = \left(44\times\sqrt{4}\right)-4 \]
\[ 85 = \frac{\left(4!+\frac{4}{.4}\right)}{.4} \]
\[ 86 = \frac{44}{.4}-4! \]
\[ 87 = \left(4!\times4\right)-\frac{4}{.\dot{4}} \]
\[ 88 = 44+44 \]
\[ 89 = \frac{\left(4!+\sqrt{4}\right)}{.4}+4! \]
\[ 90 = \frac{4!}{.\dot{4}}\times\frac{\sqrt{.\dot{4}}}{.4} \]
\[ 91 = \frac{\left(.4+\frac{4!}{\sqrt{.\dot{4}}}\right)}{.4} \]
\[ 92 = \left(44\times\sqrt{4}\right)+4 \]
\[ 93 = \left(4!\times4\right)-\sqrt{\frac{4}{.\dot{4}}} \]
\[ 94 = \left(4!-\frac{\sqrt{4}}{4}\right)\times4 \]
\[ 95 = \frac{44}{.\dot{4}}-4 \]
\[ 96 = \frac{4}{\sqrt{.4}}\times\left(\sqrt{.4}\times4!\right) \]
\[ 97 = \frac{44}{.\dot{4}}-\sqrt{4} \]
\[ 98 = 44+\frac{4!}{.\dot{4}} \]
\[ 99 = \frac{44}{\sqrt{\left(.\dot{4}\times.\dot{4}\right)}} \]
\[ 100 = \sqrt{.\dot{4}}\times\frac{4!}{\left(.4\times.4\right)} \]
\[ 101 = \frac{44}{.\dot{4}}+\sqrt{4} \]
\[ 102 = \frac{\left(4!+44\right)}{\sqrt{.\dot{4}}} \]
\[ 103 = 4+\frac{44}{.\dot{4}} \]
\[ 104 = \frac{4!}{.4}+44 \]
\[ 105 = \frac{\left(44-\sqrt{4}\right)}{.4} \]
\[ 106 = \frac{44}{.4}-4 \]
\[ 107 = \frac{\left(\left(4!\times\sqrt{4}\right)-.\dot{4}\right)}{.\dot{4}} \]
\[ 108 = \frac{\left(44+4\right)}{.\dot{4}} \]
\[ 109 = \frac{\left(44-.4\right)}{.4} \]
\[ 110 = \frac{44}{\sqrt{\left(.4\times.4\right)}} \]
\[ 111 = \frac{\left(44+.4\right)}{.4} \]
\[ 112 = 4!\times\left(\left(\sqrt{.\dot{4}}\times4\right)+\sqrt{4}\right) \]
\[ 114 = 4+\frac{44}{.4} \]
\[ 115 = \frac{\left(44+\sqrt{4}\right)}{.4} \]
\[ 116 = \left(\left(4+4!\right)\times4\right)+4 \]
\[ 117 = \frac{\left(\left(4!\times\sqrt{4}\right)+4\right)}{.\dot{4}} \]
\[ 118 = \frac{\left(4!-.4\right)}{.4}\times\sqrt{4} \]
\[ 119 = \frac{\left(4!+\left(4!-.4\right)\right)}{.4} \]
\[ 120 = \frac{\frac{\sqrt{4}}{\sqrt{.4}}}{\sqrt{.4}}\times4! \]
\[ 121 = \frac{\left(\left(.4+4!\right)+4!\right)}{.4} \]
\[ 122 = \sqrt{4}\times\frac{\left(.4+4!\right)}{.4} \]
\[ 123 = 4!+\frac{44}{.\dot{4}} \]
\[ 124 = \left(4+4!\right)+\left(4!\times4\right) \]
\[ 125 = \frac{\left(4!-4\right)}{\left(.4\times.4\right)} \]
\[ 126 = \frac{4!}{\left(.4\times.4\right)}-4! \]
\[ 128 = 4\times\left(4\times\left(4+4\right)\right) \]
\[ 130 = \frac{\left(\left(4!\times\sqrt{4}\right)+4\right)}{.4} \]
\[ 131 = \frac{\frac{4!}{.4}}{.\dot{4}}-4 \]
\[ 132 = \sqrt{\frac{4}{.\dot{4}}}\times44 \]
\[ 133 = \frac{\frac{4!}{.4}}{.\dot{4}}-\sqrt{4} \]
\[ 134 = 4!+\frac{44}{.4} \]
\[ 135 = \frac{\frac{4!}{\left(.\dot{4}\times\sqrt{.4}\right)}}{\sqrt{.4}} \]
\[ 136 = \left(4!+44\right)\times\sqrt{4} \]
\[ 137 = \sqrt{4}+\frac{\frac{4!}{.4}}{.\dot{4}} \]
\[ 138 = \frac{\left(\left(4!\times4!\right)-4!\right)}{4} \]
\[ 139 = \frac{\frac{4!}{.4}}{.\dot{4}}+4 \]
\[ 140 = 44+\left(4!\times4\right) \]
\[ 141 = \frac{\left(\left(4!\times4\right)-\sqrt{4}\right)}{\sqrt{.\dot{4}}} \]
\[ 142 = \frac{4!}{\frac{4}{4!}}-\sqrt{4} \]
\[ 143 = \frac{\left(\left(4!\times4!\right)-4\right)}{4} \]
\[ 144 = 4!\times\frac{\left(\sqrt{4}+.4\right)}{.4} \]
\[ 145 = \frac{\left(\left(4!\times4!\right)+4\right)}{4} \]
\[ 146 = \frac{4!}{\left(.4\times.4\right)}-4 \]
\[ 147 = \frac{\left(\sqrt{4}+\left(4!\times4\right)\right)}{\sqrt{.\dot{4}}} \]
\[ 148 = \frac{4!}{\left(.4\times.4\right)}-\sqrt{4} \]
\[ 149 = \frac{\left(\frac{4!}{.4}-.4\right)}{.4} \]
\[ 150 = \frac{4!}{\left(.4\times\sqrt{\left(.4\times.4\right)}\right)} \]
\[ 151 = \frac{\left(\frac{4!}{.4}+.4\right)}{.4} \]
\[ 152 = \frac{4!}{\left(.4\times.4\right)}+\sqrt{4} \]
\[ 153 = \frac{\left(4!+44\right)}{.\dot{4}} \]
\[ 154 = \frac{4!}{\left(.4\times.4\right)}+4 \]
\[ 155 = \frac{\left(\sqrt{4}+\frac{4!}{.4}\right)}{.4} \]
\[ 156 = \left(4!\times4\right)+\frac{4!}{.4} \]
\[ 159 = 4!+\frac{\frac{4!}{.4}}{.\dot{4}} \]
\[ 160 = \frac{4!}{\frac{.4}{\sqrt{.\dot{4}}}}\times4 \]
\[ 162 = \frac{4!}{\frac{\left(4-.\dot{4}\right)}{4!}} \]
\[ 165 = \frac{\frac{44}{.4}}{\sqrt{.\dot{4}}} \]
\[ 168 = 4\times\left(44-\sqrt{4}\right) \]
\[ 170 = \frac{\left(4!+44\right)}{.4} \]
\[ 172 = \left(4\times44\right)-4 \]
\[ 174 = 4!+\frac{4!}{\left(.4\times.4\right)} \]
\[ 175 = \frac{\left(4+4!\right)}{\left(.4\times.4\right)} \]
\[ 176 = \sqrt{\left(4\times4\right)}\times44 \]
\[ 178 = \sqrt{4}+\left(4\times44\right) \]
\[ 180 = 4+\left(4\times44\right) \]
\[ 184 = \left(44+\sqrt{4}\right)\times4 \]
\[ 188 = \left(\left(4+4\right)\times4!\right)-4 \]
\[ 189 = \frac{\left(\frac{4!}{.4}+4!\right)}{.\dot{4}} \]
\[ 190 = \left(\left(4+4\right)\times4!\right)-\sqrt{4} \]
\[ 192 = 4\times\left(44+4\right) \]
\[ 194 = \left(\left(4+4\right)\times4!\right)+\sqrt{4} \]
\[ 195 = \frac{\left(4!+\frac{4!}{.\dot{4}}\right)}{.4} \]
\[ 196 = 4+\left(\left(4+4\right)\times4!\right) \]
\[ 198 = \frac{\left(44\times\sqrt{4}\right)}{.\dot{4}} \]
\[ 200 = \left(4\times44\right)+4! \]
\[ 204 = 4!\times\left(\frac{\sqrt{4}}{.\dot{4}}+4\right) \]
\[ 207 = \frac{\left(\left(4!\times4\right)-4\right)}{.\dot{4}} \]
\[ 208 = 4\times\left(\left(4!\times\sqrt{4}\right)+4\right) \]
\[ 210 = \frac{\left(\frac{4!}{.4}+4!\right)}{.4} \]
\[ 212 = \left(\frac{4!}{.\dot{4}}\times4\right)-4 \]
\[ 214 = \left(\frac{4!}{.\dot{4}}\times4\right)-\sqrt{4} \]
\[ 215 = \frac{\left(\left(4!\times4\right)-.\dot{4}\right)}{.\dot{4}} \]
\[ 216 = \frac{\left(4-.4\right)}{.4}\times4! \]
\[ 217 = \frac{\left(\left(4!\times4\right)+.\dot{4}\right)}{.\dot{4}} \]
\[ 218 = \left(\frac{4!}{.\dot{4}}\times4\right)+\sqrt{4} \]
\[ 220 = \frac{\sqrt{4}}{\frac{.4}{44}} \]
\[ 222 = \frac{444}{\sqrt{4}} \]
\[ 224 = \left(4+4!\right)\times\left(4+4\right) \]
\[ 225 = \frac{\frac{4!}{\sqrt{.\dot{4}}}}{\left(.4\times.4\right)} \]
\[ 230 = \frac{\left(\left(4!\times4\right)-4\right)}{.4} \]
\[ 232 = 4\times\left(\frac{4!}{.\dot{4}}+4\right) \]
\[ 234 = \frac{\left(4\times\left(4!+\sqrt{4}\right)\right)}{.\dot{4}} \]
\[ 235 = \frac{\left(\left(4!\times4\right)-\sqrt{4}\right)}{.4} \]
\[ 236 = \frac{4}{\frac{.4}{4!}}-4 \]
\[ 238 = \frac{4}{\frac{.4}{4!}}-\sqrt{4} \]
\[ 239 = \frac{\left(\left(4!\times4\right)-.4\right)}{.4} \]
\[ 240 = 4!\times\frac{\frac{4}{\sqrt{.4}}}{\sqrt{.4}} \]
\[ 241 = \frac{\left(\left(4!\times4\right)+.4\right)}{.4} \]
\[ 242 = \sqrt{4}+\frac{4}{\frac{.4}{4!}} \]
\[ 243 = \frac{\left(\frac{\sqrt{4}}{.\dot{4}}\times4!\right)}{.\dot{4}} \]
\[ 244 = \frac{\left(.4+4!\right)}{.4}\times4 \]
\[ 245 = \frac{\left(\sqrt{4}+\left(4!\times4\right)\right)}{.4} \]
\[ 248 = 4\times\left(\sqrt{4}+\frac{4!}{.4}\right) \]
\[ 250 = \frac{\left(4+\left(4!\times4\right)\right)}{.4} \]
\[ 252 = \frac{\left(4+4!\right)}{\frac{.\dot{4}}{4}} \]
\[ 254 = \left(.\dot{4}\times\left(4!\times4!\right)\right)-\sqrt{4} \]
\[ 256 = \left(\left(4\times4\right)\times4\right)\times4 \]
\[ 258 = \sqrt{4}+\left(.\dot{4}\times\left(4!\times4!\right)\right) \]
\[ 260 = \frac{\left(4!+\sqrt{4}\right)}{\frac{.4}{4}} \]
\[ 264 = \frac{\left(44\times4!\right)}{4} \]
\[ 270 = \frac{\left(4!+\left(4!\times4\right)\right)}{.\dot{4}} \]
\[ 272 = 4\times\left(4!+44\right) \]
\[ 275 = \frac{44}{\left(.4\times.4\right)} \]
\[ 276 = \frac{\left(\left(4!\times4!\right)-4!\right)}{\sqrt{4}} \]
\[ 280 = \left(4+4!\right)\times\frac{4}{.4} \]
\[ 284 = \frac{\left(4!\times4!\right)}{\sqrt{4}}-4 \]
\[ 286 = \frac{\left(\left(4!\times4!\right)-4\right)}{\sqrt{4}} \]
\[ 287 = \frac{\left(\left(4!\times4!\right)-\sqrt{4}\right)}{\sqrt{4}} \]
\[ 288 = 4!\times\left(\left(4+4\right)+4\right) \]
\[ 289 = \frac{\left(\sqrt{4}+\left(4!\times4!\right)\right)}{\sqrt{4}} \]
\[ 290 = \frac{\left(\left(4!\times4!\right)+4\right)}{\sqrt{4}} \]
\[ 292 = \frac{\left(4!\times4!\right)}{\sqrt{4}}+4 \]
\[ 296 = 444\times\sqrt{.\dot{4}} \]
\[ 300 = \frac{\sqrt{4}}{\left(.4\times.4\right)}\times4! \]
\[ 304 = \left(\left(4!\times.\dot{4}\right)+\sqrt{4}\right)\times4! \]
\[ 312 = 4!\times\left(\frac{4}{.\dot{4}}+4\right) \]
\[ 320 = \left(\left(4!-4\right)\times4\right)\times4 \]
\[ 324 = \frac{\frac{4!}{.\dot{4}}}{4}\times4! \]
\[ 336 = 4!\times\left(\frac{4}{.4}+4\right) \]
\[ 352 = 44\times\left(4+4\right) \]
\[ 360 = \left(\left(4!\times4\right)\times4\right)-4! \]
\[ 368 = 4\times\left(\left(4!\times4\right)-4\right) \]
\[ 375 = \frac{4!}{\left(\left(.4\times.4\right)\times.4\right)} \]
\[ 376 = \left(\left(4!\times4\right)-\sqrt{4}\right)\times4 \]
\[ 380 = \left(\left(4!\times4\right)\times4\right)-4 \]
\[ 382 = \left(\left(4!\times4\right)\times4\right)-\sqrt{4} \]
\[ 384 = \left(4!\times\sqrt{\left(4\times4\right)}\right)\times4 \]
\[ 386 = \left(\left(4!\times4\right)\times4\right)+\sqrt{4} \]
\[ 388 = \left(\left(4!\times4\right)\times4\right)+4 \]
\[ 392 = \left(\sqrt{4}+\left(4!\times4\right)\right)\times4 \]
\[ 396 = \frac{44}{.\dot{4}}\times4 \]
\[ 400 = 4\times\left(4+\left(4!\times4\right)\right) \]
\[ 408 = \left(\left(4!\times4\right)\times4\right)+4! \]
\[ 416 = \left(4\times\left(4!+\sqrt{4}\right)\right)\times4 \]
\[ 420 = 444-4! \]
\[ 432 = \left(\left(4\times4\right)+\sqrt{4}\right)\times4! \]
\[ 440 = \frac{4}{\frac{.4}{44}} \]
\[ 442 = 444-\sqrt{4} \]
\[ 446 = \sqrt{4}+444 \]
\[ 448 = \left(\sqrt{.\dot{4}}\times\left(4+4!\right)\right)\times4! \]
\[ 450 = \frac{\left(4!-4\right)}{\left(.\dot{4}-.4\right)} \]
\[ 456 = \left(\left(4!-4\right)\times4!\right)-4! \]
\[ 464 = 4!\times\left(\left(4!-\sqrt{.\dot{4}}\right)-4\right) \]
\[ 468 = 4!+444 \]
\[ 472 = \left(4-4!\right)\times\left(.4-4!\right) \]
\[ 476 = \left(\left(4!-4\right)\times4!\right)-4 \]
\[ 478 = \left(\left(4!-4\right)\times4!\right)-\sqrt{4} \]
\[ 480 = 4!\times\left(44-4!\right) \]
\[ 482 = \left(\left(4!-4\right)\times4!\right)+\sqrt{4} \]
\[ 484 = 4+\left(\left(4!-4\right)\times4!\right) \]
\[ 486 = \frac{\frac{4!}{.\dot{4}}}{.\dot{4}}\times4 \]
\[ 488 = \left(.4+4!\right)\times\left(4!-4\right) \]
\[ 495 = \frac{\left(4!-\sqrt{4}\right)}{\left(.\dot{4}-.4\right)} \]
\[ 496 = \left(\left(4!-4\right)+\sqrt{.\dot{4}}\right)\times4! \]
\[ 504 = 4!+\left(\left(4!-4\right)\times4!\right) \]
\[ 512 = \left(.\dot{4}\times\left(4!\times4!\right)\right)\times\sqrt{4} \]
\[ 516 = \left(4!\times4!\right)-\frac{4!}{.4} \]
\[ 520 = \left(4!+\sqrt{4}\right)\times\left(4!-4\right) \]
\[ 522 = \left(4!\times4!\right)-\frac{4!}{.\dot{4}} \]
\[ 524 = \left(4!\times\left(4!-\sqrt{4}\right)\right)-4 \]
\[ 525 = \frac{\left(4!-\sqrt{.\dot{4}}\right)}{\left(.\dot{4}-.4\right)} \]
\[ 526 = \left(4!\times\left(4!-\sqrt{4}\right)\right)-\sqrt{4} \]
\[ 528 = \frac{\left(44\times4!\right)}{\sqrt{4}} \]
\[ 530 = \sqrt{4}+\left(4!\times\left(4!-\sqrt{4}\right)\right) \]
\[ 531 = \frac{\left(4!-.4\right)}{\left(.\dot{4}-.4\right)} \]
\[ 532 = \left(4!\times4!\right)-44 \]
\[ 536 = 4!\times\left(4!-\frac{\sqrt{.\dot{4}}}{.4}\right) \]
\[ 538 = \frac{4!}{\left(.\dot{4}-.4\right)}-\sqrt{4} \]
\[ 540 = \frac{\frac{4!}{.4}}{.\dot{4}}\times4 \]
\[ 542 = \frac{4!}{\left(.\dot{4}-.4\right)}+\sqrt{4} \]
\[ 544 = 4!\times\left(\left(4!-\sqrt{.\dot{4}}\right)-\sqrt{.\dot{4}}\right) \]
\[ 548 = \left(\left(4!\times4!\right)-4!\right)-4 \]
\[ 549 = \frac{\left(.4+4!\right)}{\left(.\dot{4}-.4\right)} \]
\[ 550 = \left(\left(4!\times4!\right)-4!\right)-\sqrt{4} \]
\[ 552 = 4!\times\left(4!-\frac{4}{4}\right) \]
\[ 554 = \left(4!\times4!\right)+\left(\sqrt{4}-4!\right) \]
\[ 555 = \frac{\left(\sqrt{.\dot{4}}+4!\right)}{\left(.\dot{4}-.4\right)} \]
\[ 556 = \left(\left(4!\times4!\right)-4!\right)+4 \]
\[ 558 = \left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)-\sqrt{4} \]
\[ 560 = \left(4!\times4!\right)-\left(4\times4\right) \]
\[ 562 = \sqrt{4}+\left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right) \]
\[ 564 = 4!\times\left(4!-\frac{\sqrt{4}}{4}\right) \]
\[ 566 = \left(4!\times4!\right)-\frac{4}{.4} \]
\[ 567 = \left(4!\times4!\right)-\frac{4}{.\dot{4}} \]
\[ 568 = \left(4!\times4!\right)-\left(4+4\right) \]
\[ 570 = \left(4!\times4!\right)-\frac{4!}{4} \]
\[ 571 = \left(4!\times4!\right)-\frac{\sqrt{4}}{.4} \]
\[ 572 = \left(4!\times4!\right)-\sqrt{\left(4\times4\right)} \]
\[ 573 = \left(4!\times4!\right)-\sqrt{\frac{4}{.\dot{4}}} \]
\[ 574 = \left(4!\times4!\right)+\left(\sqrt{4}-4\right) \]
\[ 575 = \left(4!\times4!\right)-\frac{4}{4} \]
\[ 576 = \frac{\left(\left(\sqrt{.4}\times4!\right)\times4!\right)}{\sqrt{.4}} \]
\[ 577 = \left(4!\times4!\right)+\frac{4}{4} \]
\[ 578 = \left(\left(4!\times4!\right)-\sqrt{4}\right)+4 \]
\[ 579 = \sqrt{\frac{4}{.\dot{4}}}+\left(4!\times4!\right) \]
\[ 580 = \sqrt{\left(4\times4\right)}+\left(4!\times4!\right) \]
\[ 581 = \left(4!\times4!\right)+\frac{\sqrt{4}}{.4} \]
\[ 582 = \left(\left(4!\times4!\right)+4\right)+\sqrt{4} \]
\[ 584 = \left(\left(4!\times4!\right)+4\right)+4 \]
\[ 585 = \left(4!\times4!\right)+\frac{4}{.\dot{4}} \]
\[ 586 = \left(4!\times\left(.4+4!\right)\right)+.4 \]
\[ 588 = \left(4!+\frac{\sqrt{4}}{4}\right)\times4! \]
\[ 590 = \left(4!\times\left(\sqrt{.\dot{4}}+4!\right)\right)-\sqrt{4} \]
\[ 592 = \left(4\times4\right)+\left(4!\times4!\right) \]
\[ 594 = \sqrt{4}+\left(4!\times\left(\sqrt{.\dot{4}}+4!\right)\right) \]
\[ 596 = \left(4!-4\right)+\left(4!\times4!\right) \]
\[ 598 = \left(\left(4!\times4!\right)-\sqrt{4}\right)+4! \]
\[ 600 = \frac{4!}{\left(.4\times.4\right)}\times4 \]
\[ 602 = \left(4!\times4!\right)+\left(4!+\sqrt{4}\right) \]
\[ 604 = \left(\left(4!\times4!\right)+4\right)+4! \]
\[ 608 = 4!\times\left(4!+\sqrt{\left(.\dot{4}\times4\right)}\right) \]
\[ 612 = \left(4!+\frac{\sqrt{.\dot{4}}}{.\dot{4}}\right)\times4! \]
\[ 616 = \left(4+4!\right)\times\left(4!-\sqrt{4}\right) \]
\[ 620 = \left(4!\times4!\right)+44 \]
\[ 622 = \left(4!\times\left(4!+\sqrt{4}\right)\right)-\sqrt{4} \]
\[ 624 = \left(\left(4+4!\right)-\sqrt{4}\right)\times4! \]
\[ 626 = \sqrt{4}+\left(4!\times\left(4!+\sqrt{4}\right)\right) \]
\[ 628 = 4+\left(4!\times\left(4!+\sqrt{4}\right)\right) \]
\[ 630 = \frac{4!}{.\dot{4}}+\left(4!\times4!\right) \]
\[ 636 = \frac{4!}{.4}+\left(4!\times4!\right) \]
\[ 640 = \frac{.\dot{4}}{\frac{\frac{.4}{4!}}{4!}} \]
\[ 648 = \left(4!\times\left(4+4!\right)\right)-4! \]
\[ 656 = \left(4!+\left(4-\sqrt{.\dot{4}}\right)\right)\times4! \]
\[ 666 = \frac{444}{\sqrt{.\dot{4}}} \]
\[ 668 = \left(4!\times\left(4+4!\right)\right)-4 \]
\[ 670 = \left(4!\times\left(4+4!\right)\right)-\sqrt{4} \]
\[ 672 = \left(4!+\sqrt{\left(4\times4\right)}\right)\times4! \]
\[ 674 = \sqrt{4}+\left(4!\times\left(4+4!\right)\right) \]
\[ 676 = \left(4!\times\left(4+4!\right)\right)+4 \]
\[ 684 = \left(\frac{\sqrt{4}}{.\dot{4}}+4!\right)\times4! \]
\[ 688 = 4!\times\left(\left(\sqrt{.\dot{4}}+4!\right)+4\right) \]
\[ 696 = 4!+\left(4!\times\left(4+4!\right)\right) \]
\[ 704 = 44\times\left(4\times4\right) \]
\[ 720 = \left(\left(4!+\sqrt{4}\right)+4\right)\times4! \]
\[ 728 = \left(4!+\sqrt{4}\right)\times\left(4+4!\right) \]
\[ 768 = \left(4\times\left(4+4\right)\right)\times4! \]
\[ 784 = \left(4+4!\right)\times\left(4+4!\right) \]
\[ 792 = \left(4!+\frac{4}{.\dot{4}}\right)\times4! \]
\[ 810 = \frac{\frac{4!}{\sqrt{.\dot{4}}}}{\left(.\dot{4}-.4\right)} \]
\[ 816 = \left(4!+\frac{4}{.4}\right)\times4! \]
\[ 828 = \frac{\left(\left(4!\times4!\right)-4!\right)}{\sqrt{.\dot{4}}} \]
\[ 832 = 4!\times\left(\left(4!\times.\dot{4}\right)+4!\right) \]
\[ 840 = \frac{\left(4!\times4!\right)}{\sqrt{.\dot{4}}}-4! \]
\[ 848 = \frac{\left(4!-.\dot{4}\right)}{\sqrt{.\dot{4}}}\times4! \]
\[ 858 = \frac{\left(\left(4!\times4!\right)-4\right)}{\sqrt{.\dot{4}}} \]
\[ 860 = \frac{\left(4!\times4!\right)}{\sqrt{.\dot{4}}}-4 \]
\[ 861 = \frac{\left(\left(4!\times4!\right)-\sqrt{4}\right)}{\sqrt{.\dot{4}}} \]
\[ 862 = \frac{\left(4!\times4!\right)}{\sqrt{.\dot{4}}}-\sqrt{4} \]
\[ 863 = \frac{\left(\left(4!\times4!\right)-\sqrt{.\dot{4}}\right)}{\sqrt{.\dot{4}}} \]
\[ 864 = \left(\frac{4!}{.\dot{4}}\times4\right)\times4 \]
\[ 865 = \frac{\left(\sqrt{.\dot{4}}+\left(4!\times4!\right)\right)}{\sqrt{.\dot{4}}} \]
\[ 866 = \frac{\left(4!\times4!\right)}{\sqrt{.\dot{4}}}+\sqrt{4} \]
\[ 867 = \frac{\left(\sqrt{4}+\left(4!\times4!\right)\right)}{\sqrt{.\dot{4}}} \]
\[ 868 = \frac{\left(4!\times4!\right)}{\sqrt{.\dot{4}}}+4 \]
\[ 870 = \frac{\left(\left(4!\times4!\right)+4\right)}{\sqrt{.\dot{4}}} \]
\[ 880 = \left(4!-4\right)\times44 \]
\[ 888 = \sqrt{4}\times444 \]
\[ 896 = \left(\left(\sqrt{4}-.\dot{4}\right)\times4!\right)\times4! \]
\[ 900 = \frac{\left(4!+\left(4!\times4!\right)\right)}{\sqrt{.\dot{4}}} \]
\[ 912 = 4!\times\left(\sqrt{4}+\frac{4!}{\sqrt{.\dot{4}}}\right) \]
\[ 936 = \frac{\left(4!+\sqrt{4}\right)}{\sqrt{.\dot{4}}}\times4! \]
\[ 960 = \frac{4!}{\frac{.4}{\sqrt{.\dot{4}}}}\times4! \]
\[ 968 = 44\times\left(4!-\sqrt{4}\right) \]
\[ 990 = \frac{44}{\left(.\dot{4}-.4\right)} \]
\[ 999 = \frac{444}{.\dot{4}} \]
\[ 1008 = \left(44-\sqrt{4}\right)\times4! \]
\[ 1024 = \left(\left(4!\times4\right)\times.\dot{4}\right)\times4! \]
\[ 1032 = \left(44\times4!\right)-4! \]
\[ 1040 = 4!\times\left(44-\sqrt{.\dot{4}}\right) \]
\[ 1052 = \left(44\times4!\right)-4 \]
\[ 1054 = \left(44\times4!\right)-\sqrt{4} \]
\[ 1056 = \sqrt{\left(4!\times4!\right)}\times44 \]
\[ 1058 = \left(44\times4!\right)+\sqrt{4} \]
\[ 1060 = 4+\left(44\times4!\right) \]
\[ 1072 = \left(44+\sqrt{.\dot{4}}\right)\times4! \]
\[ 1080 = 4!+\left(44\times4!\right) \]
\[ 1104 = 4!\times\left(44+\sqrt{4}\right) \]
\[ 1110 = \frac{444}{.4} \]
\[ 1120 = \left(\sqrt{4}\times\left(4!-\sqrt{.\dot{4}}\right)\right)\times4! \]
\[ 1128 = \left(\left(4!\times4!\right)\times\sqrt{4}\right)-4! \]
\[ 1136 = \left(\left(4!-\sqrt{.\dot{4}}\right)+4!\right)\times4! \]
\[ 1144 = 44\times\left(4!+\sqrt{4}\right) \]
\[ 1148 = \left(\left(4!\times4!\right)\times\sqrt{4}\right)-4 \]
\[ 1150 = \left(\left(4!\times4!\right)\times\sqrt{4}\right)-\sqrt{4} \]
\[ 1152 = 4!\times\left(44+4\right) \]
\[ 1154 = \left(\left(4!\times4!\right)\times\sqrt{4}\right)+\sqrt{4} \]
\[ 1156 = \left(\left(4!\times4!\right)\times\sqrt{4}\right)+4 \]
\[ 1160 = \sqrt{4}\times\left(\left(4!\times4!\right)+4\right) \]
\[ 1168 = \left(\sqrt{.\dot{4}}+\left(4!\times\sqrt{4}\right)\right)\times4! \]
\[ 1176 = 4!+\left(\left(4!\times4!\right)\times\sqrt{4}\right) \]
\[ 1184 = \left(\sqrt{4}\times\left(\sqrt{.\dot{4}}+4!\right)\right)\times4! \]
\[ 1188 = \frac{\left(4!\times\left(4!-\sqrt{4}\right)\right)}{.\dot{4}} \]
\[ 1200 = \frac{\left(4!-4\right)}{.4}\times4! \]
\[ 1215 = \frac{4!}{\left(\left(.\dot{4}-.4\right)\times.\dot{4}\right)} \]
\[ 1232 = 44\times\left(4+4!\right) \]
\[ 1242 = \frac{\left(\left(4!\times4!\right)-4!\right)}{.\dot{4}} \]
\[ 1248 = \left(\left(4!\times\sqrt{4}\right)+4\right)\times4! \]
\[ 1260 = \frac{\left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)}{.\dot{4}} \]
\[ 1272 = \frac{4!}{.\dot{4}}\times\left(4!-.\dot{4}\right) \]
\[ 1280 = 4!\times\left(\frac{4!}{.\dot{4}}-\sqrt{.\dot{4}}\right) \]
\[ 1287 = \frac{\left(\left(4!\times4!\right)-4\right)}{.\dot{4}} \]
\[ 1292 = \frac{\left(4!\times4!\right)}{.\dot{4}}-4 \]
\[ 1294 = \frac{\left(4!\times4!\right)}{.\dot{4}}-\sqrt{4} \]
\[ 1295 = \frac{\left(\left(4!\times4!\right)-.\dot{4}\right)}{.\dot{4}} \]
\[ 1296 = \frac{\left(4!\times\sqrt{\left(4!\times4!\right)}\right)}{.\dot{4}} \]
\[ 1297 = \frac{\left(\left(4!\times4!\right)+.\dot{4}\right)}{.\dot{4}} \]
\[ 1298 = \sqrt{4}+\frac{\left(4!\times4!\right)}{.\dot{4}} \]
\[ 1300 = \frac{\left(4!\times4!\right)}{.\dot{4}}+4 \]
\[ 1305 = \frac{\left(\left(4!\times4!\right)+4\right)}{.\dot{4}} \]
\[ 1312 = 4!\times\left(\frac{4!}{.\dot{4}}+\sqrt{.\dot{4}}\right) \]
\[ 1320 = \left(4!-\sqrt{4}\right)\times\frac{4!}{.4} \]
\[ 1332 = \frac{\left(4!\times\left(\sqrt{.\dot{4}}+4!\right)\right)}{.\dot{4}} \]
\[ 1344 = 4!\times\left(\frac{4!}{.4}-4\right) \]
\[ 1350 = \frac{\left(4!+\left(4!\times4!\right)\right)}{.\dot{4}} \]
\[ 1380 = \frac{\left(\left(4!\times4!\right)-4!\right)}{.4} \]
\[ 1392 = 4!\times\left(\frac{4!}{.\dot{4}}+4\right) \]
\[ 1400 = \frac{\left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)}{.4} \]
\[ 1404 = \frac{\left(4!\times\left(4!+\sqrt{4}\right)\right)}{.\dot{4}} \]
\[ 1408 = \left(\left(.\dot{4}+\sqrt{4}\right)\times4!\right)\times4! \]
\[ 1416 = \frac{\left(4!-.4\right)}{\frac{.4}{4!}} \]
\[ 1424 = \left(\frac{4!}{.4}-\sqrt{.\dot{4}}\right)\times4! \]
\[ 1430 = \frac{\left(\left(4!\times4!\right)-4\right)}{.4} \]
\[ 1435 = \frac{\left(\left(4!\times4!\right)-\sqrt{4}\right)}{.4} \]
\[ 1436 = \frac{\left(4!\times4!\right)}{.4}-4 \]
\[ 1438 = \frac{\left(4!\times4!\right)}{.4}-\sqrt{4} \]
\[ 1439 = \frac{\left(\left(4!\times4!\right)-.4\right)}{.4} \]
\[ 1440 = 4!\times\frac{4!}{\sqrt{\left(.4\times.4\right)}} \]
\[ 1441 = \frac{\left(\left(4!\times4!\right)+.4\right)}{.4} \]
\[ 1442 = \sqrt{4}+\frac{\left(4!\times4!\right)}{.4} \]
\[ 1444 = 4+\frac{\left(4!\times4!\right)}{.4} \]
\[ 1445 = \frac{\left(\sqrt{4}+\left(4!\times4!\right)\right)}{.4} \]
\[ 1450 = \frac{\left(\left(4!\times4!\right)+4\right)}{.4} \]
\[ 1456 = 4!\times\left(\frac{4!}{.4}+\sqrt{.\dot{4}}\right) \]
\[ 1464 = \frac{\left(4!\times\left(.4+4!\right)\right)}{.4} \]
\[ 1480 = \frac{\left(\sqrt{.\dot{4}}+4!\right)}{.4}\times4! \]
\[ 1488 = \left(\sqrt{4}+\frac{4!}{.4}\right)\times4! \]
\[ 1500 = \frac{\left(4!+\left(4!\times4!\right)\right)}{.4} \]
\[ 1512 = \frac{\left(4+4!\right)}{.\dot{4}}\times4! \]
\[ 1536 = \left(4!\times4\right)\times\left(4\times4\right) \]
\[ 1560 = \frac{\left(4!\times\left(4!+\sqrt{4}\right)\right)}{.4} \]
\[ 1584 = \frac{44}{\sqrt{.\dot{4}}}\times4! \]
\[ 1632 = \left(4!+44\right)\times4! \]
\[ 1680 = \frac{4!}{\frac{.4}{\left(4+4!\right)}} \]
\[ 1728 = \left(\left(4!\times4\right)-4!\right)\times4! \]
\[ 1776 = 444\times4 \]
\[ 1872 = \left(4!+\frac{4!}{.\dot{4}}\right)\times4! \]
\[ 1920 = \left(\left(4!-4\right)\times4!\right)\times4 \]
\[ 1936 = 44\times44 \]
\[ 1944 = \frac{\frac{\left(4!\times4!\right)}{.\dot{4}}}{\sqrt{.\dot{4}}} \]
\[ 2016 = 4!\times\left(\frac{4!}{.4}+4!\right) \]
\[ 2048 = 4!\times\left(4!\times\left(4-.\dot{4}\right)\right) \]
\[ 2112 = \left(44\times\sqrt{4}\right)\times4! \]
\[ 2160 = \frac{\frac{\left(4!\times4!\right)}{.4}}{\sqrt{.\dot{4}}} \]
\[ 2208 = \left(\left(4!\times4\right)-4\right)\times4! \]
\[ 2240 = \left(4\times\left(4!-\sqrt{.\dot{4}}\right)\right)\times4! \]
\[ 2256 = \left(\left(4!\times4\right)-\sqrt{4}\right)\times4! \]
\[ 2280 = \left(4\times\left(4!\times4!\right)\right)-4! \]
\[ 2288 = 4\times\left(\left(4!\times4!\right)-4\right) \]
\[ 2296 = 4\times\left(\left(4!\times4!\right)-\sqrt{4}\right) \]
\[ 2300 = \left(4\times\left(4!\times4!\right)\right)-4 \]
\[ 2302 = \left(4\times\left(4!\times4!\right)\right)-\sqrt{4} \]
\[ 2304 = \left(4!\times4!\right)\times\sqrt{\left(4\times4\right)} \]
\[ 2306 = \sqrt{4}+\left(4\times\left(4!\times4!\right)\right) \]
\[ 2308 = \left(4\times\left(4!\times4!\right)\right)+4 \]
\[ 2312 = 4\times\left(\sqrt{4}+\left(4!\times4!\right)\right) \]
\[ 2320 = \left(\left(4!\times4!\right)+4\right)\times4 \]
\[ 2328 = 4!+\left(4\times\left(4!\times4!\right)\right) \]
\[ 2352 = 4!\times\left(\sqrt{4}+\left(4!\times4\right)\right) \]
\[ 2368 = \left(4!\times\left(\sqrt{.\dot{4}}+4!\right)\right)\times4 \]
\[ 2376 = \frac{44}{.\dot{4}}\times4! \]
\[ 2400 = \left(4+\left(4!\times4\right)\right)\times4! \]
\[ 2496 = \left(4\times\left(4!+\sqrt{4}\right)\right)\times4! \]
\[ 2560 = \left(4!\times4!\right)\times\left(.\dot{4}+4\right) \]
\[ 2592 = \frac{\left(4!\times4!\right)}{.\dot{4}}\times\sqrt{4} \]
\[ 2640 = \frac{4!}{\frac{.4}{44}} \]
\[ 2688 = \left(4!\times\left(4+4!\right)\right)\times4 \]
\[ 2880 = 4!\times\left(4!+\left(4!\times4\right)\right) \]
\[ 2916 = \frac{\frac{4!}{.\dot{4}}}{.\dot{4}}\times4! \]
\[ 3240 = \frac{\left(4!\times4!\right)}{\left(.4\times.\dot{4}\right)} \]
\[ 3456 = \frac{4!}{\frac{4}{4!}}\times4! \]
\[ 3600 = \frac{4!}{\left(.4\times.4\right)}\times4! \]
\[ 4224 = \left(44\times4!\right)\times4 \]
\[ 4444 = 4444 \]
\[ 4608 = \left(4+4\right)\times\left(4!\times4!\right) \]
\[ 5184 = \frac{\left(4!\times4!\right)}{.\dot{4}}\times4 \]
\[ 5760 = \frac{4}{\frac{.4}{4!}}\times4! \]
\[ 6144 = \left(4!\times\left(4!\times4!\right)\right)\times.\dot{4} \]
\[ 6912 = \frac{\left(4!\times4!\right)}{\sqrt{4}}\times4! \]
\[ 9216 = \left(4\times4\right)\times\left(4!\times4!\right) \]
\[ 10656 = 4!\times444 \]
\[ 11520 = \left(\left(4!-4\right)\times4!\right)\times4! \]
\[ 12672 = \left(4!\times\left(4!-\sqrt{4}\right)\right)\times4! \]
\[ 12960 = \frac{4!}{\frac{\left(.\dot{4}-.4\right)}{4!}} \]
\[ 13248 = \left(\left(4!\times4!\right)-4!\right)\times4! \]
\[ 13440 = \left(\left(4!-\sqrt{.\dot{4}}\right)\times4!\right)\times4! \]
\[ 13568 = \left(\left(4!-.\dot{4}\right)\times4!\right)\times4! \]
\[ 13728 = \left(\left(4!\times4!\right)-4\right)\times4! \]
\[ 13776 = 4!\times\left(\left(4!\times4!\right)-\sqrt{4}\right) \]
\[ 13800 = \left(4!\times\left(4!\times4!\right)\right)-4! \]
\[ 13808 = \left(\left(4!\times4!\right)-\sqrt{.\dot{4}}\right)\times4! \]
\[ 13820 = \left(4!\times\left(4!\times4!\right)\right)-4 \]
\[ 13822 = \left(4!\times\left(4!\times4!\right)\right)-\sqrt{4} \]
\[ 13824 = \left(4!\times4!\right)\times\sqrt{\left(4!\times4!\right)} \]
\[ 13826 = \sqrt{4}+\left(4!\times\left(4!\times4!\right)\right) \]
\[ 13828 = 4+\left(4!\times\left(4!\times4!\right)\right) \]
\[ 13840 = \left(\sqrt{.\dot{4}}+\left(4!\times4!\right)\right)\times4! \]
\[ 13848 = \left(4!\times\left(4!\times4!\right)\right)+4! \]
\[ 13872 = \left(\sqrt{4}+\left(4!\times4!\right)\right)\times4! \]
\[ 13920 = \left(\left(4!\times4!\right)+4\right)\times4! \]
\[ 14080 = \left(\left(.\dot{4}+4!\right)\times4!\right)\times4! \]
\[ 14208 = \left(4!\times\left(\sqrt{.\dot{4}}+4!\right)\right)\times4! \]
\[ 14400 = \left(4!+\left(4!\times4!\right)\right)\times4! \]
\[ 14976 = \left(4!\times\left(4!+\sqrt{4}\right)\right)\times4! \]
\[ 16128 = \left(4!\times\left(4+4!\right)\right)\times4! \]
\[ 20736 = \frac{\left(4!\times4!\right)}{\sqrt{.\dot{4}}}\times4! \]
\[ 25344 = 4!\times\left(44\times4!\right) \]
\[ 27648 = \left(4!\times\sqrt{4}\right)\times\left(4!\times4!\right) \]
\[ 31104 = \left(4!\times4!\right)\times\frac{4!}{.\dot{4}} \]
\[ 34560 = \frac{4!}{.4}\times\left(4!\times4!\right) \]
\[ 55296 = \left(4\times\left(4!\times4!\right)\right)\times4! \]
\[ 331776 = \left(4!\times\left(4!\times4!\right)\right)\times4! \]

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