数で遊ぼう

　課題　
　４を必ず４回使い，数学記号を利用することにより，０から２００までの数をつくってみよう
　
$0=4+4-4-4=4!+4!-4!-4=44-44=4^4-4^4=4\times4-4\times4$
$1=4\div4\times4\div4=4^4\div4^4=(4+4)\div(4+4)=44\div44$
$2=4\div4+4\div4$
$3=(4+4+4)\div4$
$4=(4-4)\times4+4=(4-4)\div4+4=4\times4^{4-4}$
$5=(4\times4+4)\div4=4!\div4-4\div4$
$6=(4+4)\div4+4=4!\div4+4-4=4!\times4\div4\div4$
$7=44\div4-4=4!\div4+4\div4$
$8=4+4+4-4$
$9=4\div4+4+4$
$10=(44-4)\div4$
$11=44\div\sqrt{{4}\times{4}}$ 　
$12=4\times4-\sqrt{{4}\times{4}}=(44+4)\div{4}=4\times{4}-\sqrt{4}-\sqrt{4}$
$13=44\div{4}+\sqrt{4}$
$14=4!\div{4}+4+4=4\times{4}-4\div{\sqrt{4}}={\sqrt{4}}^4-4\div{\sqrt{4}}=4^{\sqrt{4}}-4\div{\sqrt{4}}$
$15=4\times{4}-4\div{4}=44\div{4}+4={\sqrt{4}}^4-4\div{4},\ 4^{\sqrt{4}}-4\div{4}$
$16=4+4+4+4=4\times{4}+4-4=4\times{4}\times{4}\div{4}=(4!+4!)\div{4}+4$
$17=4\times{4}+4\div{4}$
$18=4\times{4}+4\div{\sqrt{4}}=4!-4-4\div{sqrt{4}}$
$19=4!-4-4\div{4}$
$20=4\times{4}+\sqrt{4}+\sqrt{4}=4!-4+4-4$
$21=4!-4+4\div{4}=4!-4!\div{4}\div{{\sqrt{4}}$
$22=4\times{4}+4+\sqrt{4}=44\times{\sqrt{4}}\div{4}$
$23=4!-4^{4-4}=4!-4\div{\sqrt{4}}\div{\sqrt{4}}$
$24=4\times{4}+4+4=44\div{{\sqrt{4}}+\sqrt{4}=4!+(4-4)\times{4}$
$25=(4\div{4}+4)^{\sqrt{4}}=4!+\sqrt{4\times{4}}\div{4}=4!+4^{4-4}$
$26=4!+(4+4)\div{4}=4!+4-4+\sqrt{4}$
$27=4!+\sqrt{4}+4\div{4}$
$28=4!+4+4-4$
$29=4!+4+4\div{4}$
$30=4!+\sqrt{4}+\sqrt{4}+\sqrt{4}=4!+4+4-\sqrt{4}$
$31=4!+(4!+4)\div4=4!+4!!-4\div4=4!!\times4-4\div4$
$32=4\times{\sqrt4}\times{\sqrt4}\times{\sqrt4}=4\times4+4\times4=4!!+4!!+4!!+4!!=4!\times{\sqrt4}-4\times4=4!!\times4+4-4$
　　 $=4!+4!!+4-4$
$33=4!!\times4+4\div4=4!+4!!+4\div4$
$34=4!+4!!+4\div{\sqrt4}=4!+4!!+4-\sqrt4$
$35=4!+44\div4$
$36=4!!\times4+sqrt4+\sqrt4=4!+4\times4-4=44-4-4$
$37=4!+(4!+\sqrt4)\div{\sqrt4}$
$38=4!!\times4+4+\sqrt4=4!+4!!+4+\sqrt4$
$39= 4!+{}_{4+\sqrt4}\mathrm{C}_{\sqrt4}$
$40=4\times(4+4+\sqrt4)=4!!\times4+4+4=4!!\times4+4\times\sqrt4$ 　
$41=44-4!\div4!!$
$42=4!+4\times4+\sqrt4=44-4+\sqrt4=4!\times{\sqrt4}-4-\sqrt4=4!\times{\sqrt4}-4!\div4$
$43=44-4\div4$
$44=44+4-4=4!+4\times4+4=4!\times{\sqrt4}-\sqrt4-\sqrt4$
$45=44+4\div4$
$46=44+4-\sqrt4=44+4\div\sqrt4=4!\times{\sqrt4}-4+\sqrt4$
$47=4!\times{\sqrt4}-4\div4=44+4!\div4!!$
$48=44+\sqrt4+\sqrt4=4!\times{\sqrt4}+4-4=4!+4\times\sqrt{4\times4}=4\times4\times4!\div4!!$
$49=4!\times{\sqrt4}+4\div4=(4!!-4\div4)^{\sqrt4}$
$50=4!\times{\sqrt4}+4-\sqrt4=44+4+\sqrt4$
$51=4!\times{\sqrt4}+4!\div{4!!}=4!+4!+4!\div{4!!}$
$52=44+4+4=4!\times{\sqrt4}+\sqrt{4\times4}$ 　
$53={}_{4!!} \mathrm{P} _{\sqrt4}-4!\div{4!!}$
$54={}_{4!!} \mathrm{P} _{\sqrt4}-4+\sqrt4=4!+4!+4+\sqrt4$
$55={}_{4!!} \mathrm{P} _{\sqrt4}-4\div4$
$56=4!+4!+4+4=44+4!!+4={}_{4!!} \mathrm{P} _{\sqrt4}+4-4$
$57={}_{4!!} \mathrm{P} _{\sqrt4}+4\div4$
$58={}_{4!!} \mathrm{P} _{\sqrt4}+4-\sqrt4=4!!\times{4!!}-4-sqrt4$
$59={}_{4!!} \mathrm{P} _{\sqrt4}+4!\div{4!!}$
$60={}_{4!!} \mathrm{P} _{\sqrt4}+\sqrt4+\sqrt4=44+4\times4=4!!\times{4!!}-sqrt4-sqrt4$
$61=4!!\times{4!!}-4!\div{4!!}$
$62=4!!\times{4!!}-4+\sqrt4={}_{4!!} \mathrm{P} _{\sqrt4}+4+\sqrt4=4^4\div4-\sqrt4$
$63=4!!\times{4!!}-4\div4$
$64=4!!\times{4!!}+4-4={}_{4!!} \mathrm{P} _{\sqrt4}+4+4=4!+4!+4\times4=44+4!-4=4^4\div(\sqrt4+\sqrt4)$
$65=4!!\times{4!!}+4\div4$
$66=4!\times{4!}+4-\sqrt4={}_{4!!} \mathrm{P} _{\sqrt4}+4!!+\sqrt4$
$67=4!\times{4!}+4!\div{4!!}$
$68=4!\times{4!}+\sqrt4+\sqrt4$
$69={}_{4!!}\mathrm{C}_{4}-4\div4$
$70=4!\times{4!}+4+\sqrt4$
$71={}_{4!!}\mathrm{C}_{4}+4\div4$
$72={}_{4!!}\mathrm{C}_{4}+4-\sqrt4=(\sqrt4+\sqrt4)!\times4!\div{4!!}=4!\times{4!}+4+4$
$73={}_{4!!}\mathrm{C}_{4}+4!\div{4!!}=(4!\div{4!!})^4-4!!$
$74={}_{4!!}\mathrm{C}_{4}+\sqrt4+\sqrt4$
$75=(4!!)!!!-4-4\div4={}_{4! }\mathrm{H}_{(4\div{\sqrt4})} \div4$
$76={}_{4!!}\mathrm{C}_{4}+4+\sqrt4$
$77=(4!!)!!!-4+4\div4$
$78=(4!!)!!!+4-4-sqrt4={}_{4!!}\mathrm{C}_{4}+4+4$
$79=(4!!)!!!-4^{4-4}$
$80=(4!!)!!!-4\times(4-4)=\sqrt4\times(44-4)={}_{4!!}\mathrm{C}_{4}+4!!+\sqrt4$
$81=(4!!)!!!+4^{4-4}$
$82=(4!!)!!!+4-4+\sqrt4={}_{4!!}\mathrm{C}_{4}+4!!+4$
$83=(4!!)!!!+4-4\div4$
$84=(4!!)!!!+4+4-4=(44-\sqrt4)\times{\sqrt4}=4!\times4-4!!-4$
$85=(4!!)!!!+4+4\div4$
$86=(4!!)!!!+4+4-\sqrt4=44\times\sqrt4-\sqrt4={}_{4!!}\mathrm{C}_{4}+4!-4!!=4!\times4-4!!-\sqrt4$
$87=(4!!)!!!+4!!-4\div4$
$88=44\times4\div{sqrt4}=(4!!)!!!+4!!+4-4$
$89=(4!!)!!!+4!!+4\div4$
$90=(4!!)!!!+4+4+\sqrt4=4!\times4-4-\sqrt4={}_{4!!}\mathrm{C}_{4}+4!!-\sqrt4-\sqrt4$
$91=(4!!)!!!+4!!+{4!}\div{4!!}$
$92=(4!!)!!!+4+4+4=4!\times4-\sqrt4-\sqrt4={}_{4!!}\mathrm{C}_{4}+4!!-4+\sqrt4$
$93=4!\times4-{4!}\div{4!!}$
$94=4!\times4-4+\sqrt4=(4!!)!!!+4\times4-\sqrt4$
$95={4!}\times4-{4\div{4}$
$96=4!\times4+4-4=(4!!\!)!!!+4\times({\sqrt4+\sqrt4)$
$97=4!\times4+4\div4$
$98=4!\times4+4-\sqrt4=(4!!)!!!+4\times4+\sqrt4$
$99=4!\times4+{4!\div{4!!}$
$100=4!\times4+\sqrt4+\sqrt4=(4!!)!!!+4\times4+4$
$101=(4!!)!!!+4!-{4!}\div{4!!}$
$102=(4!!)!!!+4!-4\div\sqrt4$
$103=(4!!)!!!+4!-4\div4$
$104=(4!!)!!!+4!-4+4$
$105=(4!!)!!!+4!+4\div4$
$106=(4!!)!!!+4!+4\div\sqrt4$
$107=(4!!)!!!+4!+{4!}\div{4!!}$
$108=(4!!)!!!+4!+\sqrt4+\sqrt4$
$109=(4+4)!\div{(4!!)!!}+4$
$110=(4!!)!!!+4!+4+\sqrt4$
$111=444\div4$
$112=(4!!)!!!+4!+4+4=(4!!)!!!+4^{\sqrt4}\times{\sqrt4}$
$113=(4+4)!\div{(4!!)!!}+4!!$
$114=(4!!)!!!+4!+\sqrt4+4!!$
$115=(4!!)!\div{(4!!)!!}+4!!+\sqrt4$
$116=(4!!)!!!+4!+4+4!!$
$117=(4!!)!\div{(4!!)!!}+4!!+4$
$118=(4!!)!!!+4!+4\times4$
$119=({(4!!)!!!}\div{4!!})!!!!-4\div4$
$120=(4!!)!!!+4!+4!!+4!!={\sqrt4}^{4!!}\div{\sqrt4}-4!!=(4!!)!!!!\times4-4-4$
$121=({(4!!)!!!}\div{4!!})!!!!+4\div4$
$122=({(4!!)!!!}\div{4!!})!!!!+4\div{\sqrt4}=(4!!)!!!!\times4-4-\sqrt4$
$123=({(4!!)!!!}\div{4!!})!!!!+4!\div4!!$
$124=({(4!!)!!!}\div{4!!})!!!!+\sqrt4+\sqrt4=(4!!)!!!!\times4-\sqrt4-\sqrt4$
$125=(4!!)!!!!\times4-4!\times4!!$
$126=({(4!!)!!!}\div{4!!})!!!!+4+\sqrt4=(4!!)!!!!\times4-4+\sqrt4$
$127=(4!!)!!!!\times4-4\div4$
$128=\sqrt4^{4!!-4\div4}=({(4!!)!!!}\div{4!!})!!!!+4+4=(4!!)!!!!\times4+4-4$
$129=(4!!)!!!!\times4+4\div4$
$130=({(4!!)!!!}\div{4!!})!!!!+4!!+\sqrt4=(4!!)!!!!\times4+4-\sqrt4$
$131=(4!!)!!!!\times4+4!\div4!!$
$132=(4!!)!!!!\times4+\sqrt4+\sqrt4$
$133=(4!!)!\div(4!!)!!+(4!!)!!!!-4$
$134=(4!!)!!!!\times4+4+\sqrt4$
$135=(4!!)!\div(4!!)!!+(4!!)!!!!-\sqrt4$
$136=(4!!)!!!!\times4+4+4$
$137=(4!!)!\div(4!!)!!+4!!\times4$
$138=(4!!)!!!!\times4+4!!+\sqrt4$
$139=(4!!)!\div(4!!)!!+(4!!)!!!!+\sqrt4$
$140=(4!!)!!!!\times4+4!!+4$
$141=(4!!)!\div(4!!)!!+(4!!)!!!!+4$
$142=(4!!)!!!+4!!\times4!!-\sqrt4$
$143=(4!\times4!-4)\div4$
$144=(4!!)!!!!\times4+4\times4$
$145=(4!!)!\div(4!!)!!-(4!!)!!!\div{\sqrt4}$
$146=(4!!)!!!+4!!\times4!!+\sqrt4$
$147=\[({}_{(4!!)!!!}\mathrm{C}_{\sqrt4}+(4!!)!!)\div4!\]=4!\times4!!-(\sqrt{\sqrt{(4!)!!!\div(4!!)!}})!!!!$
$148=(4!!)!!!!\times4+4!-4=(4!!)!!!+4!!\times4!!+4$
$149=(4!!)!\div\(4!!)!!+44$
$150=(4!!)!!!!\times4+4!-\sqrt4=(4+4)!!!+{}_{4!!}\mathrm{C}_{4}$
$151=(4!!)!!!+(4!!)!!!-\sqrt{\sqrt{(4!)!!!\div(4!!)!}}$
$152=(4!!)!!!+(4!!)!!!-4-4=(4!!)!!!!\times(\sqrt4+\sqrt4)+4!=(4!!)!!!+{}_{4!!}\mathrm{C}_{4}+\sqrt4$
$153=(4!!)!\div(4!!)!!+4!+4!$
$154=(4!!)!!!+(4!!)!!!-4-\sqrt4=(4!!)!!!!\times4+4!+\sqrt4=(4!!)!!!+{}_{4!!}\mathrm{C}_{4}+4$
$155=\[((4!!)!!!\times4!!-\sqrt{(4!)!!})\div4\]$
$156=(4!!)!!!+(4!!)!!!-\sqrt4-\sqrt4=(4!!)!!!!\times4+4!+4$
$157=(4!!)!!!+(4!!)!!!-4!\div4!!$
$158=(4!!)!!!+(4!!)!!!-4+\sqrt4=(4!!)!!!+{}_{4!!}\mathrm{C}_{4}+4!!$
$159=(4!!)!!!+(4!!)!!!-4\div4$
$160=(4+4)!!!+(4+4)!!!=(4!!)!!!!\times4+4!+4!!=(4!!)!!!+{}_{4!!} \mathrm{P} _{\sqrt4}+4!$
$161=(4!!)!!!+(4!!)!!!+4\div4$
$162=(4!!)!!!+(4!!)!!!+4-\sqrt4$
$163=(4!!)!!!+(4!!)!!!+4!\div4!!$
$164=(4!!)!!!+(4!!)!!!+\sqrt4+\sqrt4$
$165=\[(4!!)!!!+(4!!)!!!+\sqrt{4!+4}\]$
$166=(4!!)!!!+(4!!)!!!+4+\sqrt4$
$167=\[(4!!)!!!+(4!!)!!!+\sqrt{{}_{4!!} \mathrm{P} _{\sqrt4}}\]$
$168=(4!!)!!!+(4!!)!!!+4+4$
$169=(4!!)!!!+(4!!)!!!+\sqrt{\sqrt{(4!)!!!\div(4!!)!}}=(4!!)!\div\(4!!)!!+(4!!)!!!!\times\sqrt4$
$170=(4!!)!!!+(4!!)!!!+4!!+\sqrt4$
$171=\[((4!!)!!-(4!!)!!!!)\div\sqrt4-sqrt{4!}\]=\[44\times4-\sqrt{4!}\]$
$172=(4!!)!!!+(4!!)!!!+4!!+4=44\times4-4$
$173={}_{4!!} \mathrm{H} _4\div\sqrt4+4!!$
$174={}_{4!!}\mathrm{C}_{4}+(4!!)!!!+4!=44\times4-\sqrt4$
$175=(4!!)!\div\(4!!)!!+{}_{4!!}\mathrm{C}_{4}$
$176=(4!!)!!!+(4!!)!!!+4!!+4!!$
$177=((4!!)!!-(4!!)!!!!+\sqrt4)\div\sqrt4$
$178=44\times4+\sqrt4$
$179=((4!!)!!-4!-sqrt4)\div\sqrt4$
$180=(4!!)!!!+(4!!)!!!+(4!!)!!!\div4=44\times4+4$
$181=((4!!)!!-4!+\sqrt4)\div\sqrt4$
$182=((4!!)!!-4!+4)\div\sqrt4$
$183=((4!!)!!-2)\div\sqrt4-4!!$
$184=((4!!)!!-4!!-4!!)\div\sqrt4$
$185=((4!!)!!+2)\div\sqrt4-4!!$
$186=((4!!)!!-4!!-4)\div\sqrt4$
$187=((4!!)!!-4!!-\sqrt4)\div\sqrt4$
$188=((4!!)!!-4-4)\div\sqrt4$
$189=((4!!)!!-4-\sqrt4)\div\sqrt4$
$190=((4!!)!!-\sqrt4-\sqrt4)\div\sqrt4$
$191=((4!!)!!-4+\sqrt4)\div\sqrt4=((4!!)!!+\sqrt4)\div\sqrt4-\sqrt4$
$192=(4!!)!!\div\sqrt4+4-4=(4!!)!!!+(4!!)!!!+((\sqrt4+\sqrt4)!!)!!!!$
$193=((4!!)!!+4-\sqrt4)\div\sqrt4=((4!!)!!-\sqrt4)\div\sqrt4+\sqrt4$
$194=(4!!)!!\div\sqrt4+4-\sqrt4=(4!!)!!!+(4!!)!!!+(4!!)!!!!+\sqrt4$
$195=((4!!)!!-\sqrt4)\div\sqrt4+4=((4!!)!!+\sqrt4)\div\sqrt4+\sqrt4$
$196=(4!!)!!\div\sqrt4+\sqr4+\sqrt4=(4!!)!!!+(4!!)!!!+(4!!)!!!!+4$
$197=((4!!)!!+\sqrt4)\div\sqrt4+4$
$198=(4!!)!!\div\sqrt4+4+\sqrt4$
$199=((4!!)!!-\sqrt4)\div\sqrt4+4!!$
$200=(4!!)!!\div\sqrt4+4+4=(4!!)!!!+(4!!)!!!+(4!!)!!!!+4!!$

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