Question

aa+bb+cc+dd=d4d, Hallar a+b+c-d

Answer 1

aa+bb+cc+dd=d4d

(a*10 + a) + (b*10 + b) + (c*10 + c) + (d*10 + d) = d*100 + 40 + d

= d*10*10 + 40 + d

= d*10*(1+9) + 40 + d

= d*10 + d*10*9 + 40 + d

a*10 + a + b*10 + b + c*10 + c + d*10 + d = d*10 + d*10*9 + 40 + d

a*10 + a + b*10 + b + c*10 + c = d*10*9 + 40

a*10 + a + b*10 + b + c*10 + c = d*10*(1 + 8) + 40

a*10 + a + b*10 + b + c*10 + c = d*10 + d*10*8 + 40

a*10 + a + b*10 + b + c*10 + c - d*10 = d*10*8 + 10*4

10*(a + b +c - d) + (a + b +c) = 10*4*(d*2 + 1)

10*(a + b + c - d) = 10*4*(d*2 + 1) - (a + b +c)

a + b + c - d = 4*(2*d + 1) - (a + b + c)/10