If
a(10b + c) = d(10e + f) = g(10h + i),
find the value of a,b,c,d,e,f,g,h,i
if value is beetween 1 to 9.

• Let k = a(10b + c) = d(10e + f) = g(10h + i).
  
  k cannot be odd because then a, c, d, f, g and i have to be odd too. But there are only 5 odd vales between 1 to 9. So k is even and ( a or c) and (d or f) and (g or i) are even.
  k cannot be multiple of 5 because then ( a or c) and (d or f) and (g or i) are even have to be multiple of 5. But there is only one multiple of 5 between 1 to 9.
  I don't know how to continue this reasoning.
  But with the help of Excel I discovered that the solution is:
  k = 162 = 3(5·10 + 4) = 9(1·10 + 8) = 6 (2·10 + 7).
  
• 11 years agoHelpfull: Yes(0) No(4)