Răspuns:
Explicație pas cu pas:
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xyz + yzx + zxy = 666
(100x+10y+z) + (100y+10z+y) +(100z+10x+y) = 666
(100x+10x+x) +(100y+10y+y) + (100z+10z+z) = 666
111x + 111y+111z = 666
111 × ( x + y + z ) = 666
x + y + z = 666 : 111
x + y + z = 6 => 0 < x. y, z < 5
x = 1 ⇒ y + z = 5 ⇒ y = 1; 2 ; 3 , iar z = 3; 2; 1
x = 2 ⇒ y + z = 4 ⇒ y = 1; 2; 3; iar z = 3; 2; 1
x = 3 ⇒ y + z = 3 ⇒ y = 1; 2; iar z = 2; 1
Asadar numerele sunt:
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xyz: 123; 132; 213; 231; 312; 321 cu cifre diferite
dar si 114; 141; 411 si 222
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Verific:
114 + 141 + 411 = 666
123 + 231 + 312 = 666
Raspuns:
Explicație pas cu pas:
xyz+yzx+zxy=666
100x+10y+z+100y+10z+x+100z+10+y=666
111x+111x+111z=666
111(x+y+z)=666
x+y+z=6
x=6 nu merge
x=5 nu merge
x=4 | y+z=2 => y=1,z=1 | z=1,y=1
x=3 | y+z=3 => y=1,z=2 | y=2,z=1
x=2 | y+z=4 => y=1,z=3 | y=2,z=2 | z=1,y=3
x=1 | y+x+z=5 => y=1,z=4 | y=2,z=3 | y=3,z=2 | y=4,z=1
