Plan A

各種組合(不要列舉)

書名:Thinking Mathematically
作者:John.Mason

增減數字個數

a^2+b^2+c^2=d^2+e^2+f^2=g^2+h^2+i^2

(100a+10d+g)^2+(100b+10e+h)^2+(100c+10f+j)^2=
(100g+10d+a)^2+(100h+10e+b)^2+(100j+10f+c)^2

(100g+10d+a)^2=
10000g^2+100d^2+a^2+2000gd+200ga+20da

(100a+10d+g)^2=
10000a^2+100d^2+g^2+2000ad+200ag+20dg

(100a+10d+g)^2+(100b+10e+h)^2+(100c+10f+j)^2=
(100d+10g+a)^2+(100e+10h+b)^2+(100f+10j+c)^2

(100a+10d+g)^2=
10000a^2+100d^2+g^2+2000ad+200ag+20dg

(100d+10g+a)^2=
10000d^2+100g^2+a^2+2000gd+200da+20ga

a^2+b^2+c^2+d^2=e^2+f^2+g^2+h^2

(10a+e)^2+(10b+f)^2+(10c+g)^2+(10d+h)^2=(10e+a)^2+(10f+b)^2+(10g+c)^2+(10h+d)^2

(100a^2+20ae+e^2)+(100b^2+20bf+f^2)+(100c^2+20cg+g^2)+(100d^2+20dh+h^2)=(100e^2+20ae+a^2)+(100f^2+20bf+b^2)+(100g^2+20cg+c^2)+(100h^2+20dh+d^2)

(100a^2+e^2)+(100b^2+f^2)+(100c^2+g^2)+(100d^2+h^2)=
(100e^2+a^2)+(100f^2+b^2)+(100g^2+c^2)+(100h^2+d^2)

a^3+b^3+c^3=d^3+e^3+f^3

(10a+d)^3+(10b+e)^3+(10c+f)^3=
(10d+a)^3+(10e+b)^3+(10f+c)^3

(1000a^3+300a^2d+30ad^2+d^3)+(1000b^3+300b^2e+30be^2+e^3)+(1000c^3+300c^2f+30cf^2+f^3) = (1000d^3+300d^2a+30da^2+a^3)+(1000e^3+300e^2b+30eb^2+b^3)+(1000f^3+300f^2c+30fc^2+c^3)

(999a^3+270a^2d)+(999b^3+270b^2e)+(999c^3+270c^2f)=(999d^3+270d^2a)+(999e^3+270e^2b)+(999f^3+270f^2c)

(10a+d)^2+(10b+e)^2+(10c+f)^2=(10g+h)^2+(10i+j)^2+(10k+l)^2

a^2+b^2+c^2=d^2+e^2+f^2
且a,b,c,d,e,f皆為二位數

(100a+d)^2+(100b+e)^2+(100c+f)^2=
(100d+a)^2+(100e+b)^2+(100f+c)^2

(10000a^2+200ad+d^2)+(10000b^2+200be+e^2)+(10000c^2+200cf+f^2)=(10000d^2+200ad+a^2)+(10000e^2+200be+b^2)+(10000f^2+200cf+c^2)

(10000a^2+d^2)+(10000b^2+e^2)+(10000c^2+f^2)=(10000d^2+a^2)+(10000e^2+b^2)+(10000f^2+c^2)

9999a^2+9999b^2+9999c^2=
9999d^2+9999e^2+9999f^2

99a^2+99b^2+99c^2+99d^2=
99e^2+99f^2+99g^2+99h^2

四次方

a^4+b^4+c^4=d^4+e^4+f^4

(10a+d)^4+(10b+e)^4+(10c+f)^4=
(10d+a)^4+(10e+b)^4+(10f+c)^4

(10000a^4+4000a^3d+600a^2d^2+40ad^3+d^4)(10000b^4+4000b^3e+600b^2e^2+40be^3+e^4)(10000c^4+4000c^3f+600c^2f^2+40cf^3+f^4)=(10000d^4+4000d^3a+600d^2a^2+40da^3+a^4)(10000e^4+4000e^3b+600e^2b^2+40eb^3+b^4)(10000f^4+4000f^3c+600f^2c^2+40fc^3+c^4)

(9999a^4+3960a^3d)+(9999b^4+3960b^3e)+(9999c^4+3960c^3f)=
(9999d^4+3960d^3a)+(9999e^4+3960e^3b)+(9999c^4+3960f^3c)

a^2+b^2+c^2=d^2+e^2+f^2
且a,b,c,d,e,f皆為三位數

用任何數字來滿足下列形式之式子 a^2+b^2+c^2=d^2+e^2+f^2搭配左邊和右邊數字(用任何方法皆可)(10a+d)^2+(10b+e)^2+(10c+f)^2=(10d+a)^2+(10e+b)^2+(10f+c)^2

4^2+5^2+6^2=2^2+3^2+8^2

(100a^2+20ad+d^2)+(100b^2+20be+e^2)+(100c^2+20cf+f^2)=(100d^2+20ad+a^2)+(100e^2+20be+b^2)+(100f^2+20cf+c^2)

(100a^2+d^2)+(100b^2+e^2)+(100c^2+f^2)=
(100d^2+a^2)+(100e^2+b^2)+(100f^2+c^2)

99a^2+99b^2+99c^2=
99d^2+99e^2+99f^2

(1000a+d)^2+(1000b+e)^2+(1000c+f)^2=
(1000d+a)^2+(1000e+b)^2+(1000f+c)^2

兩個數字

a^2+b^2=c^2+d^2

(10a+c)^2+(10b+d)^2=
(10c+a)^2+(10d+b)^2

(100a^2+20ac+c^2)+(100b^2+20bd+d^2)=(100c^2+20ac+a^2)+(100d^2+20bd+b^2)

99a^2+99b^2=
99c^2+99d^2

[100(10a+d)+(10g+h)]^2+[100(10b+e)+(10i+j)]^2+[100(10c+f)+(10k+l)]^2=[100(10g+h)+(10a+d)]^2+[100(10i+j)+(10b+e)]^2+[100(10k+l)+(10c+f)]^2

(1000a+100d+10g+h)^2+(1000b+100e+10i+j)^2+(1000c+100f+10k+l)^2=(1000g+100h+10a+d)^2+(1000i+100j+10b+e)^2+(1000k+100l+10c+f)^2

(1000000a^2+10000d^2+100g^2+h^2)+(200000ad+20000ag+2000ah+2000dg+200dh+20gh)+(1000000b^2+10000e^2+100i^2+j^2)+(200000be+20000bi+2000bj+2000ei+200ej+20ij)+(1000000c^2+10000f^2+100k^2+l^2)+(200000cf+20000ck+2000cl+2000fk+200fl+20kl)=(1000000g^2+10000h^2+100a^2+d^2)+(200000gh+20000ag+2000dg+2000ah+200dh+20ad)+(1000000i^2+10000j^2+100b^2+e^2)+(200000ij+20000bi+2000ei+2000bj+200dh+20be)+(1000000k^2+10000l^2+100c^2+f^2)+(200000kl+20000ck+2000fk+2000cl+200fl+20cf)

999900a^2+9999d^2+999900b^2+9999e^2+999900c^2+9999f^2+199980ad+199980be+199980cf=999900g^2+9999h^2+999900i^2+9999j^2+999900k^2+9999l^2+199980gh+199980ij+199980kl

100a^2+20ad+d^2+100b^2+20be+e^2+100c^2+20cf+f^2=100g^2+20gh+h^2+100i^2+20ij+j^2+100k^2+20kl+l^2

Plan C

考量到上一個主題沒救了

決定做一個新的

如果這個也沒救