CMO 1981 Problem 1

For any real number $t$ , denote by $[t]$ the greatest integer which is less than or equal to $t$ . For example: $[8] = 8$ , $[\pi] = 3$ , and $[-5/2] = -3$ . Show that the equation $$[x] + [2x] + [4x] + [8x] + [16x] + [32x] = 12345$$ has no real solution.