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# Send more money. Each different letter represents a unique (different) digit from 0 to 9. Find what each letter is so the following long multiplication is true: $$ \begin{array}{} & & S & E & N & D \\ + & & M & O & R & E \\\hline & M & O & N & E & Y \end{array} $$ Discussion/hint. - If this problem is multiplication instead, is it possible? - In this adding situation, what you can conclude about the letter $M$? Think about what happens if we add two four digit numbers together. - Carrying is very important here. Analyze when we must carry, and how much can we carry each time. - If it makes it easier, you can allow the leading letter to be $0$. But usually we don't write a number with leading $0$, so avoid that. Some "simpler" ones if you like to try more, these have multiple solutions, find at least two for each: $$ \begin{array}{} & T & I & M & E \\ - & & F & O & R \\\hline & & B & E & D \end{array} $$ $$ \begin{array}{} & & & E & A & T \\ +& & S & O & M & E \\ \hline & P & I & Z & Z & A \end{array} $$ $$ \begin{array}{} & & D & U & C & K \\ + & & D & U & C & K \\ \hline & G & O & O & S & E \end{array} $$ $$ \begin{array}{} & & & C & A & T \\ \times& & & D & O & G \\ \hline & H & O & U & S & E \end{array} $$ $$ \begin{array}{} & O & F & T & E & N \\ + & & K & N & O & W \\\hline & T & H & I & N & G \end{array} $$ $$ \begin{array}{} & & U & N & I & T & E \\ + & & E & N & J & O & Y \\ \hline & N & A & T & U & R & E \end{array} $$ These have only **one solution**: $$ \begin{array}{} \\ & & P & R & E & S & S \\ + & & & L & O & S & E \\ \hline & D & A & N & G & E & R \end{array} $$ $$ \begin{array}{} & & & & N & O \\ \times & & V & E & R & Y \\ \hline & C & O & U & R & T \end{array} $$