Question:
Show that the Cryptarithm $4 \times \overline{A B}=\overline{C A B}$ does not have any solution.
Solution:
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 $\mathrm{B}$ is 0 .
Similarly, for A also, 0 is the only possible digit.
But then $A, B$ and $C$ will all be 0 .
And if $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ 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.