Show that cryptarithm $4 \times \overline{AB}=\overline{CAB}$ does not have any solution.
To do:
We have to show that cryptarithm $4 \times \overline{AB}=\overline{CAB}$ does not have any solution.
Solution:
$4 \times \overline{\mathrm{AB}}=\overline{\mathrm{CAB}}$
$\overline{\mathrm{AB}}$ is a two digit number and $\overline{\mathrm{CAB}}$ is a three digit number.
$4 \times \overline{\mathrm{AB}}=\overline{\mathrm{CAB}}$
This implies,
$ A\ B$
$\times 4$
--------------
$C\ AB$
This implies,
$4 \times B$ is a number whose units digit is $B$.
There is no such digit which when multiplied by 4 has the same number at the units place.
Hence, the given cryptarithm has no solution.
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