If TO + GO = OUT, then what is the value of T + G + O + U?Choices:- 15 11 7 18

This problem is a cryptarithm, a number-based puzzle in which a mathematical equation is given, but instead of numbers, letters are used. Each letter represents a unique digit from 0 to 9. The goal is to find the digits that make the equation true. The equation is: TO + GO = OUT.

Let's solve it step by step:

1. Since T + G results in a two-digit number (OU), T + G must be equal to or greater than 10. Therefore, T and G are 5 or greater.

2. Since O is a common digit in both the summands and the sum, the operation T + G must have resulted in a carry. Therefore, O must be 1.

3. Now, the equation becomes: 1T + 1G = 1U1. This implies that T + G = 10 + U. Since T and G are 5 or greater, U must be 0.

4. Now, we know that O = 1 and U = 0. So, T + G = 10. As T and G are different digits, the only possible combination is T = 6 and G = 4 or T = 4 and G = 6.

5. Therefore, the possible values for T + G + O + U are 6 + 4 + 1 + 0 = 11 or 4 + 6 + 1 + 0 = 11.

So, the answer is 11.