Final all the solutions for ONE + ONE = TWO each letter stands for a different digit
To find all the solutions for the equation ONE + ONE = TWO, where each letter stands for a different digit, we can use a systematic approach called "backtracking." Here's how we can proceed:
1. Assign a different digit from 0 to 9 to each of the letters O, N, E, T, and W. Since O + O must equal a number less than or equal to 9, we know that O = 1.
2. Now, we have the equation 1NE + 1NE = TWO.
3. Since O = 1, we need to find distinct digits for N, E, T, and W.
4. Begin by assigning a digit to N. Start with N = 0 and proceed with N = 2, 3, 4, ..., 9. For each value of N, calculate E, T, and W accordingly.
5. Remember that carrying can occur when adding the digits. Keep track of the carried-over digit(s) from the previous addition.
6. If at any point, we find that N = E = T = W, it means that we have assigned the same digit to multiple letters, violating the condition of the problem. In this case, we backtrack and explore the next value for N.
7. Continue this process until all possible values of N have been exhausted.
Let's go through an example step-by-step:
1. O = 1 (as determined earlier)
2. 1NE + 1NE = TWO
3. Assign N = 0:
- 10E + 10E = TWO
4. No need for carrying since both digits multiplied by 2 do not exceed 9.
5. Solving the equation: 10E + 10E = TWO
- E + E = W (equation 1)
6. We can find the solution by plugging in different values for E and computing W accordingly.
- For E = 0, equation 1 becomes 0 + 0 = W, which gives W = 0. But this cannot be the solution since W cannot be 0 according to the problem statement, as it represents the leftmost digit in the sum.
- Continue trying different values for E.
7. Trying E = 1, equation 1 becomes 1 + 1 = W, which gives W = 2.
The equation becomes 10(1) + 10(1) = TWO, which simplifies to 20 + 20 = 40, which is not valid.
Therefore, N = 0 and E = 1 does not yield a valid solution.
8. We would continue this process, assigning N = 2, 3, 4, etc., and checking if valid solutions are obtained.
By following this systematic approach, you can exhaustively search for all the possible solutions for the equation ONE + ONE = TWO, where each letter represents a different digit.