The Easiest (or the Hardest)?

Logic Level pending

The figure represents a multiplication followed by an addition.
Each of the dots is filled by a number from 1 1 to 9 9 . No digit is repeated.

Find the sum of the digits of the last row (the final answer).


This problem is a part of my set Numbers in Disguise - Cryptarithms .


The answer is 12.

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1 solution

Didn't read the question properly. If the numbers are from 0 0 to 9 9 , there will be 4 4 solutions with 2 2 final results.

\[\begin{array} {} & 1 & 7 &&& \color{blue}{1} & \color{blue}{7} &&& 1 & 8 &&& 3 & 8 \\ \times & & 2 & & \color{blue}{ \times} & & \color{blue}{4} & & \times & & 2 & & \times & & 2 \\ \hline & 3 & 4 &&& \color{blue}{6} & \color{blue}{8} &&& 3 & 6 &&& 7 & 6 \\ + & 5 & 6 & & \color{blue}{ +} & \color{blue}{2} & \color{blue}{5} & & + & 5 & 4 & & + & 1 & 4 \\ \hline & 9 & 0 & && \color{blue}{9} & \color{blue}{ 3} && & 9 & 0 & && 9 & 0 \end{array} \]

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