Provide the answer for the following Cryptarithmetic problem:   SEND +MORE MONEY"

To solve the cryptarithmetic problem $SEND + MORE = MONEY$, we assign unique digits to each letter such that the equation holds true. Let's break down the solution step by step.

Step 1: Break Down the Problem

We need to assign digits to the letters $S, E, N, D, M, O, R, Y$ such that the equation $SEND + MORE = MONEY$ is valid. Each letter represents a distinct digit (0-9), and $S$ and $M$ cannot be zero since they are leading digits.

Step 2: Relevant Concepts

We represent the words as:

$SEND = 1000S + 100E + 10N + D$

$MORE = 1000M + 100O + 10R + E$

$MONEY = 10000M + 1000O + 100N + 10E + Y$

Our equation becomes:

$1000S + 100E + 10N + D + 1000M + 100O + 10R + E = 10000M + 1000O + 100N + 10E + Y$

Step 3: Analysis and Detail

To find a solution, we need to ensure:

1. Each letter corresponds to a unique digit.
2. Leading digits $S$ and $M$ are not zero.
3. We can apply trial and error or systematic checking for different values of $S, E, N, D, M, O, R,$ and $Y$.

After testing combinations, the following assignment works:

• $S = 9$
• $E = 5$
• $N = 6$
• $D = 7$
• $M = 1$
• $O = 0$
• $R = 8$
• $Y = 2$

So:

$SEND = 9567,\quad MORE = 1085,\quad MONEY = 10652$

Step 4: Verify and Summarize

Now we verify the solution:

$9567 + 1085 = 10652$

This equation is true, confirming the assignments of the letters.

Final Answer

Thus, the solution to the cryptarithmetic problem $SEND + MORE = MONEY$ is:

$S = 9,\quad E = 5,\quad N = 6,\quad D = 7,\quad M = 1,\quad O = 0,\quad R = 8,\quad Y = 2$