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Letters for digits

A = ; B =

Question

$\begin{matrix} 4 A 4 B A + A A B 1 B B B \end{matrix}$
A=_;B=_;

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Solution

For A + A + B = B, A can be 0 or 5.

$\begin{matrix} A = 0 & A = 5 I f A = 0, 4 + B + A = B & I f A = 5, A + A + B = B ∴ 4 + B = B & 10 + B = B B c a n o n l y b e 0. & B c a n b e a n y t h i n g f r o m 0 t o 9 e x c e p t 5 B u t A = 0; & W e h a v e 1 c a r r y f o r 2 n d c o l u m n H e n c e B c a n^{'} t b e z e r o . N o t w o l e t t e r s c a n r e p r e s e n t s a m e d i g i t s . & 1 + 4 + B + A = B C a r r y 10 + B = B S i m i l a r l y, f o r 3 r d c o l u m n 1 + 4 + A = B C a r r y 10 = B \Rightarrow B = 0 ∴ A = 5; B = 0 \end{matrix}$

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