เพื่อนถามกันในไลน์ให้หาว่าต้องใส่เครื่องหมาย +-×/^ระหว่างตัวเลขยังไงบ้าง2 2 2 = 63 3 3 = 34 4 4 = 65 5 5 = 66 6 6 = 67 7 7 = 68 8 8 = 69 9 9 = 6
Operators ที่จะลองใส่เข้าไปก็มี บวก ลบ คูณ หาร แล้วก็ ยกกำลัง
In[]:=
op={"+","-","*","/","^"};
มันจะมีที่ให้ใส่อยู่สองที่ ดังนั้นที่เป็นไปได้ทั้งหมดก็คือ
In[]:=
opls=Tuples[op,2]
Out[]=
{{+,+},{+,-},{+,*},{+,/},{+,^},{-,+},{-,-},{-,*},{-,/},{-,^},{*,+},{*,-},{*,*},{*,/},{*,^},{/,+},{/,-},{/,*},{/,/},{/,^},{^,+},{^,-},{^,*},{^,/},{^,^}}
พอใส่เครื่องหมายเข้าไปแล้วมันได้ทั้งหมดตามนี้
In[]:=
all=Table[ToString[i]<>#1<>ToString[i]<>#2<>ToString[i]&@@@opls,{i,2,9}]//Flatten
Out[]=
{2+2+2,2+2-2,2+2*2,2+2/2,2+2^2,2-2+2,2-2-2,2-2*2,2-2/2,2-2^2,2*2+2,2*2-2,2*2*2,2*2/2,2*2^2,2/2+2,2/2-2,2/2*2,2/2/2,2/2^2,2^2+2,2^2-2,2^2*2,2^2/2,2^2^2,3+3+3,3+3-3,3+3*3,3+3/3,3+3^3,3-3+3,3-3-3,3-3*3,3-3/3,3-3^3,3*3+3,3*3-3,3*3*3,3*3/3,3*3^3,3/3+3,3/3-3,3/3*3,3/3/3,3/3^3,3^3+3,3^3-3,3^3*3,3^3/3,3^3^3,4+4+4,4+4-4,4+4*4,4+4/4,4+4^4,4-4+4,4-4-4,4-4*4,4-4/4,4-4^4,4*4+4,4*4-4,4*4*4,4*4/4,4*4^4,4/4+4,4/4-4,4/4*4,4/4/4,4/4^4,4^4+4,4^4-4,4^4*4,4^4/4,4^4^4,5+5+5,5+5-5,5+5*5,5+5/5,5+5^5,5-5+5,5-5-5,5-5*5,5-5/5,5-5^5,5*5+5,5*5-5,5*5*5,5*5/5,5*5^5,5/5+5,5/5-5,5/5*5,5/5/5,5/5^5,5^5+5,5^5-5,5^5*5,5^5/5,5^5^5,6+6+6,6+6-6,6+6*6,6+6/6,6+6^6,6-6+6,6-6-6,6-6*6,6-6/6,6-6^6,6*6+6,6*6-6,6*6*6,6*6/6,6*6^6,6/6+6,6/6-6,6/6*6,6/6/6,6/6^6,6^6+6,6^6-6,6^6*6,6^6/6,6^6^6,7+7+7,7+7-7,7+7*7,7+7/7,7+7^7,7-7+7,7-7-7,7-7*7,7-7/7,7-7^7,7*7+7,7*7-7,7*7*7,7*7/7,7*7^7,7/7+7,7/7-7,7/7*7,7/7/7,7/7^7,7^7+7,7^7-7,7^7*7,7^7/7,7^7^7,8+8+8,8+8-8,8+8*8,8+8/8,8+8^8,8-8+8,8-8-8,8-8*8,8-8/8,8-8^8,8*8+8,8*8-8,8*8*8,8*8/8,8*8^8,8/8+8,8/8-8,8/8*8,8/8/8,8/8^8,8^8+8,8^8-8,8^8*8,8^8/8,8^8^8,9+9+9,9+9-9,9+9*9,9+9/9,9+9^9,9-9+9,9-9-9,9-9*9,9-9/9,9-9^9,9*9+9,9*9-9,9*9*9,9*9/9,9*9^9,9/9+9,9/9-9,9/9*9,9/9/9,9/9^9,9^9+9,9^9-9,9^9*9,9^9/9,9^9^9}
In[]:=
(#<>"=6"&/@(Reap[If[ToExpression[#]6,Sow[#]]&/@all][[2,1]]))//Column
Out[]=
2+2+2=6
2+2*2=6
2+2^2=6
2*2+2=6
2^2+2=6
3*3-3=6
5+5/5=6
5/5+5=6
6+6-6=6
6-6+6=6
6*6/6=6
6/6*6=6
7-7/7=6
ลองเพิ่มรากที่สองเข้าไปด้วย
In[]:=
op={"+","-","*","/","^","^0.5+","^0.5-","^0.5*","^0.5/"};
In[]:=
opls=Tuples[op,2]
Out[]=
{{+,+},{+,-},{+,*},{+,/},{+,^},{+,^0.5+},{+,^0.5-},{+,^0.5*},{+,^0.5/},{-,+},{-,-},{-,*},{-,/},{-,^},{-,^0.5+},{-,^0.5-},{-,^0.5*},{-,^0.5/},{*,+},{*,-},{*,*},{*,/},{*,^},{*,^0.5+},{*,^0.5-},{*,^0.5*},{*,^0.5/},{/,+},{/,-},{/,*},{/,/},{/,^},{/,^0.5+},{/,^0.5-},{/,^0.5*},{/,^0.5/},{^,+},{^,-},{^,*},{^,/},{^,^},{^,^0.5+},{^,^0.5-},{^,^0.5*},{^,^0.5/},{^0.5+,+},{^0.5+,-},{^0.5+,*},{^0.5+,/},{^0.5+,^},{^0.5+,^0.5+},{^0.5+,^0.5-},{^0.5+,^0.5*},{^0.5+,^0.5/},{^0.5-,+},{^0.5-,-},{^0.5-,*},{^0.5-,/},{^0.5-,^},{^0.5-,^0.5+},{^0.5-,^0.5-},{^0.5-,^0.5*},{^0.5-,^0.5/},{^0.5*,+},{^0.5*,-},{^0.5*,*},{^0.5*,/},{^0.5*,^},{^0.5*,^0.5+},{^0.5*,^0.5-},{^0.5*,^0.5*},{^0.5*,^0.5/},{^0.5/,+},{^0.5/,-},{^0.5/,*},{^0.5/,/},{^0.5/,^},{^0.5/,^0.5+},{^0.5/,^0.5-},{^0.5/,^0.5*},{^0.5/,^0.5/}}
In[]:=
all=Table[ToString[i]<>#1<>ToString[i]<>#2<>ToString[i]&@@@opls,{i,2,9}]//Flatten
Out[]=
{2+2+2,2+2-2,2+2*2,2+2/2,2+2^2,2+2^0.5+2,2+2^0.5-2,2+2^0.5*2,2+2^0.5/2,2-2+2,2-2-2,2-2*2,2-2/2,2-2^2,2-2^0.5+2,2-2^0.5-2,2-2^0.5*2,2-2^0.5/2,2*2+2,2*2-2,2*2*2,2*2/2,2*2^2,2*2^0.5+2,2*2^0.5-2,2*2^0.5*2,2*2^0.5/2,2/2+2,2/2-2,2/2*2,2/2/2,2/2^2,2/2^0.5+2,2/2^0.5-2,2/2^0.5*2,2/2^0.5/2,2^2+2,2^2-2,2^2*2,2^2/2,2^2^2,2^2^0.5+2,2^2^0.5-2,2^2^0.5*2,2^2^0.5/2,2^0.5+2+2,2^0.5+2-2,2^0.5+2*2,2^0.5+2/2,2^0.5+2^2,2^0.5+2^0.5+2,2^0.5+2^0.5-2,2^0.5+2^0.5*2,2^0.5+2^0.5/2,2^0.5-2+2,2^0.5-2-2,2^0.5-2*2,2^0.5-2/2,2^0.5-2^2,2^0.5-2^0.5+2,2^0.5-2^0.5-2,2^0.5-2^0.5*2,2^0.5-2^0.5/2,2^0.5*2+2,2^0.5*2-2,2^0.5*2*2,2^0.5*2/2,2^0.5*2^2,2^0.5*2^0.5+2,2^0.5*2^0.5-2,2^0.5*2^0.5*2,2^0.5*2^0.5/2,2^0.5/2+2,2^0.5/2-2,2^0.5/2*2,2^0.5/2/2,2^0.5/2^2,2^0.5/2^0.5+2,2^0.5/2^0.5-2,2^0.5/2^0.5*2,2^0.5/2^0.5/2,3+3+3,3+3-3,3+3*3,3+3/3,3+3^3,3+3^0.5+3,3+3^0.5-3,3+3^0.5*3,3+3^0.5/3,3-3+3,3-3-3,3-3*3,3-3/3,3-3^3,3-3^0.5+3,3-3^0.5-3,3-3^0.5*3,3-3^0.5/3,3*3+3,3*3-3,3*3*3,3*3/3,3*3^3,3*3^0.5+3,3*3^0.5-3,3*3^0.5*3,3*3^0.5/3,3/3+3,3/3-3,3/3*3,3/3/3,3/3^3,3/3^0.5+3,3/3^0.5-3,3/3^0.5*3,3/3^0.5/3,3^3+3,3^3-3,3^3*3,3^3/3,3^3^3,3^3^0.5+3,3^3^0.5-3,3^3^0.5*3,3^3^0.5/3,3^0.5+3+3,3^0.5+3-3,3^0.5+3*3,3^0.5+3/3,3^0.5+3^3,3^0.5+3^0.5+3,3^0.5+3^0.5-3,3^0.5+3^0.5*3,3^0.5+3^0.5/3,3^0.5-3+3,3^0.5-3-3,3^0.5-3*3,3^0.5-3/3,3^0.5-3^3,3^0.5-3^0.5+3,3^0.5-3^0.5-3,3^0.5-3^0.5*3,3^0.5-3^0.5/3,3^0.5*3+3,3^0.5*3-3,3^0.5*3*3,3^0.5*3/3,3^0.5*3^3,3^0.5*3^0.5+3,3^0.5*3^0.5-3,3^0.5*3^0.5*3,3^0.5*3^0.5/3,3^0.5/3+3,3^0.5/3-3,3^0.5/3*3,3^0.5/3/3,3^0.5/3^3,3^0.5/3^0.5+3,3^0.5/3^0.5-3,3^0.5/3^0.5*3,3^0.5/3^0.5/3,4+4+4,4+4-4,4+4*4,4+4/4,4+4^4,4+4^0.5+4,4+4^0.5-4,4+4^0.5*4,4+4^0.5/4,4-4+4,4-4-4,4-4*4,4-4/4,4-4^4,4-4^0.5+4,4-4^0.5-4,4-4^0.5*4,4-4^0.5/4,4*4+4,4*4-4,4*4*4,4*4/4,4*4^4,4*4^0.5+4,4*4^0.5-4,4*4^0.5*4,4*4^0.5/4,4/4+4,4/4-4,4/4*4,4/4/4,4/4^4,4/4^0.5+4,4/4^0.5-4,4/4^0.5*4,4/4^0.5/4,4^4+4,4^4-4,4^4*4,4^4/4,4^4^4,4^4^0.5+4,4^4^0.5-4,4^4^0.5*4,4^4^0.5/4,4^0.5+4+4,4^0.5+4-4,4^0.5+4*4,4^0.5+4/4,4^0.5+4^4,4^0.5+4^0.5+4,4^0.5+4^0.5-4,4^0.5+4^0.5*4,4^0.5+4^0.5/4,4^0.5-4+4,4^0.5-4-4,4^0.5-4*4,4^0.5-4/4,4^0.5-4^4,4^0.5-4^0.5+4,4^0.5-4^0.5-4,4^0.5-4^0.5*4,4^0.5-4^0.5/4,4^0.5*4+4,4^0.5*4-4,4^0.5*4*4,4^0.5*4/4,4^0.5*4^4,4^0.5*4^0.5+4,4^0.5*4^0.5-4,4^0.5*4^0.5*4,4^0.5*4^0.5/4,4^0.5/4+4,4^0.5/4-4,4^0.5/4*4,4^0.5/4/4,4^0.5/4^4,4^0.5/4^0.5+4,4^0.5/4^0.5-4,4^0.5/4^0.5*4,4^0.5/4^0.5/4,5+5+5,5+5-5,5+5*5,5+5/5,5+5^5,5+5^0.5+5,5+5^0.5-5,5+5^0.5*5,5+5^0.5/5,5-5+5,5-5-5,5-5*5,5-5/5,5-5^5,5-5^0.5+5,5-5^0.5-5,5-5^0.5*5,5-5^0.5/5,5*5+5,5*5-5,5*5*5,5*5/5,5*5^5,5*5^0.5+5,5*5^0.5-5,5*5^0.5*5,5*5^0.5/5,5/5+5,5/5-5,5/5*5,5/5/5,5/5^5,5/5^0.5+5,5/5^0.5-5,5/5^0.5*5,5/5^0.5/5,5^5+5,5^5-5,5^5*5,5^5/5,5^5^5,5^5^0.5+5,5^5^0.5-5,5^5^0.5*5,5^5^0.5/5,5^0.5+5+5,5^0.5+5-5,5^0.5+5*5,5^0.5+5/5,5^0.5+5^5,5^0.5+5^0.5+5,5^0.5+5^0.5-5,5^0.5+5^0.5*5,5^0.5+5^0.5/5,5^0.5-5+5,5^0.5-5-5,5^0.5-5*5,5^0.5-5/5,5^0.5-5^5,5^0.5-5^0.5+5,5^0.5-5^0.5-5,5^0.5-5^0.5*5,5^0.5-5^0.5/5,5^0.5*5+5,5^0.5*5-5,5^0.5*5*5,5^0.5*5/5,5^0.5*5^5,5^0.5*5^0.5+5,5^0.5*5^0.5-5,5^0.5*5^0.5*5,5^0.5*5^0.5/5,5^0.5/5+5,5^0.5/5-5,5^0.5/5*5,5^0.5/5/5,5^0.5/5^5,5^0.5/5^0.5+5,5^0.5/5^0.5-5,5^0.5/5^0.5*5,5^0.5/5^0.5/5,6+6+6,6+6-6,6+6*6,6+6/6,6+6^6,6+6^0.5+6,6+6^0.5-6,6+6^0.5*6,6+6^0.5/6,6-6+6,6-6-6,6-6*6,6-6/6,6-6^6,6-6^0.5+6,6-6^0.5-6,6-6^0.5*6,6-6^0.5/6,6*6+6,6*6-6,6*6*6,6*6/6,6*6^6,6*6^0.5+6,6*6^0.5-6,6*6^0.5*6,6*6^0.5/6,6/6+6,6/6-6,6/6*6,6/6/6,6/6^6,6/6^0.5+6,6/6^0.5-6,6/6^0.5*6,6/6^0.5/6,6^6+6,6^6-6,6^6*6,6^6/6,6^6^6,6^6^0.5+6,6^6^0.5-6,6^6^0.5*6,6^6^0.5/6,6^0.5+6+6,6^0.5+6-6,6^0.5+6*6,6^0.5+6/6,6^0.5+6^6,6^0.5+6^0.5+6,6^0.5+6^0.5-6,6^0.5+6^0.5*6,6^0.5+6^0.5/6,6^0.5-6+6,6^0.5-6-6,6^0.5-6*6,6^0.5-6/6,6^0.5-6^6,6^0.5-6^0.5+6,6^0.5-6^0.5-6,6^0.5-6^0.5*6,6^0.5-6^0.5/6,6^0.5*6+6,6^0.5*6-6,6^0.5*6*6,6^0.5*6/6,6^0.5*6^6,6^0.5*6^0.5+6,6^0.5*6^0.5-6,6^0.5*6^0.5*6,6^0.5*6^0.5/6,6^0.5/6+6,6^0.5/6-6,6^0.5/6*6,6^0.5/6/6,6^0.5/6^6,6^0.5/6^0.5+6,6^0.5/6^0.5-6,6^0.5/6^0.5*6,6^0.5/6^0.5/6,7+7+7,7+7-7,7+7*7,7+7/7,7+7^7,7+7^0.5+7,7+7^0.5-7,7+7^0.5*7,7+7^0.5/7,7-7+7,7-7-7,7-7*7,7-7/7,7-7^7,7-7^0.5+7,7-7^0.5-7,7-7^0.5*7,7-7^0.5/7,7*7+7,7*7-7,7*7*7,7*7/7,7*7^7,7*7^0.5+7,7*7^0.5-7,7*7^0.5*7,7*7^0.5/7,7/7+7,7/7-7,7/7*7,7/7/7,7/7^7,7/7^0.5+7,7/7^0.5-7,7/7^0.5*7,7/7^0.5/7,7^7+7,7^7-7,7^7*7,7^7/7,7^7^7,7^7^0.5+7,7^7^0.5-7,7^7^0.5*7,7^7^0.5/7,7^0.5+7+7,7^0.5+7-7,7^0.5+7*7,7^0.5+7/7,7^0.5+7^7,7^0.5+7^0.5+7,7^0.5+7^0.5-7,7^0.5+7^0.5*7,7^0.5+7^0.5/7,7^0.5-7+7,7^0.5-7-7,7^0.5-7*7,7^0.5-7/7,7^0.5-7^7,7^0.5-7^0.5+7,7^0.5-7^0.5-7,7^0.5-7^0.5*7,7^0.5-7^0.5/7,7^0.5*7+7,7^0.5*7-7,7^0.5*7*7,7^0.5*7/7,7^0.5*7^7,7^0.5*7^0.5+7,7^0.5*7^0.5-7,7^0.5*7^0.5*7,7^0.5*7^0.5/7,7^0.5/7+7,7^0.5/7-7,7^0.5/7*7,7^0.5/7/7,7^0.5/7^7,7^0.5/7^0.5+7,7^0.5/7^0.5-7,7^0.5/7^0.5*7,7^0.5/7^0.5/7,8+8+8,8+8-8,8+8*8,8+8/8,8+8^8,8+8^0.5+8,8+8^0.5-8,8+8^0.5*8,8+8^0.5/8,8-8+8,8-8-8,8-8*8,8-8/8,8-8^8,8-8^0.5+8,8-8^0.5-8,8-8^0.5*8,8-8^0.5/8,8*8+8,8*8-8,8*8*8,8*8/8,8*8^8,8*8^0.5+8,8*8^0.5-8,8*8^0.5*8,8*8^0.5/8,8/8+8,8/8-8,8/8*8,8/8/8,8/8^8,8/8^0.5+8,8/8^0.5-8,8/8^0.5*8,8/8^0.5/8,8^8+8,8^8-8,8^8*8,8^8/8,8^8^8,8^8^0.5+8,8^8^0.5-8,8^8^0.5*8,8^8^0.5/8,8^0.5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