数で遊ぼう

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課題 

 3を必ず3回使い,数学記号を利用することにより,0から10までの数をつくってみよう

0=(3-3)\div3=(3-3)\times3

1=3^{3-3}=3-3!\div3

2=(3+3)\div3=3-3\div3

3=3\times3\div3=3\times3-3!=3+3-3

4=3+3\div3=(3!+3!)\div3 

5=3+3!\div3=3!-3\div3

6=3!+3-3=3\times3-3

7=3!+3\div3 

8=3!+3!\div3

9=3+3+3

10=3.\dot3\times3 
 

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!!
 

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,201から300までの数をつくってみよう


201=((4!!)!!+\sqrt4)\div\sqrt4+4!!
202=((4!!)!!+4!-4)\div\sqrt4=((4!!)!!+4!)\div\sqrt4-sqrt4
203=((4!!)!!+4!-sqrt4)\div\sqrt4
204=((4!!)!!+(\sqrt4+\sqrt4)!)\div\sqrt4
205=({}_{4!!} \mathrm{H} _4+(4!!)!!!)\div\sqrt4
206=((4!!)!!+4!)\div\sqrt4+sqrt4
207=((4!!)!!+(4!!)!!!!-\sqrt4)\div\sqrt4
208=((4!!)!!+4!)\div\sqrt4+4
209=((4!!)!!+(4!!)!!!!+\sqrt4)\div\sqrt4
210=((4!!)!!+{}_{4!!} \mathrm{H} _{\sqrt4})\div\sqrt4
211=({}_{4!!} \mathrm{P} _{4}+4!!)\div{4!!}
212=((4!!)!!+(4!!)!!!!+4!!)\div\sqrt4
213=({}_{4!!} \mathrm{P} _{4}+4!)\div{4!!}
214=((4!!)!!+44)\div\sqrt4
215=((4!!)!!-sqrt4)\div\sqrt4+4!
216=((4!!)!!+4!+4!)\div\sqrt4
217=((4!!)!!+sqrt4)\div\sqrt4+4!
218={}_{4!!} \mathrm{P} _{4}\div{4!!}+4!!
219=\[4^4-(4!!)!!!!-\sqrt{4!}\]
220=((4!!)!!+(4!!)!!!-4!)\div\sqrt4
221=\[4^4-(4!!)!!!!-\sqrt{4!!}\]
222=4^4-(4!!)!!!!-\sqrt4
223=((4!!)!!-\sqrt4)\div\sqrt4+(4!!)!!!!
224=4^4-((\sqrt{4\times4})!!)!!!!
225=((4!!)!!+\sqrt4)\div\sqrt4+(4!!)!!!!
226=4^4-(4!!)!!!!+\sqrt4