Question

Solve each of the following Cryptarithms:

  3 7
+ A B
  9 A

Answer 1

Two possible values of A are: 
\[(i) \text{ If } 7 + B \leq 9\]
\[ \therefore 3 + A = 9 \]
\[ \Rightarrow A = 6\]
\[\text{ But if } A = 6, 7 + B \text{ must be larger than }9 . \text{ Hence, it is impossible . }\]
\[(ii)\text{ If }7 + B \geq 9\]
\[ \therefore 1 + 3 + A = 9\]
\[ \Rightarrow A = 5\]
\[\text{ If }A = 5\text{ and }7 + B = 5,\text{ B must be }8\]
\[ \therefore A = 5, B = 8\]