Question

Show that the Cryptarithm

\[4 \times \overline{{AB}} = \overline{{CAB}}\] does not have any solution.

Answer 1

0 is the only unit digit number, which gives the same 0 at the unit digit when multiplied by 4 . So, the possible value of B is 0. 
Similarly, for A also, 0 is the only possible digit.
But then A, B and C will all be 0.
And if A, B and C become 0, these numbers cannot be of two - digit or three - digit.
Therefore, both will become a one - digit number.
Thus, there is no solution possible.