Show that two WRONG's can make a RIGHT. Replace each different letter in the addition problem with a different digit. It is required that O=zero.
To solve this problem, we need to replace each different letter with a different digit, with the constraint that the letter O represents zero.
Let's break down the problem step by step:
1. Start by establishing the given addition problem: WRONG + WRONG = RIGHT.
2. Since "O" represents zero, we can rewrite the problem as WRO0G + WRO0G = RIGHT.
3. Now, let's look at the rightmost column, which is the least significant digit (units digit). Adding two zeros (0 + 0) will always result in zero (0). So, we know that the letter "T" in RIGHT must be zero.
4. We have WRO0G + WRO0G = RIG0T.
5. Moving to the next column, which is the tens digit, we need to find two digits that, when multiplied by 2, will result in a number ending in zero (the letter "G" in "WRONG" is multiplied by 2 and carries over to the tens digit). One such pair is 5 and 0, or 6 and 0. Either digit can be assigned to the letter "G". For simplicity, let's choose 5.
6. Now we have WRO50 + WRO50 = RIG0T.
7. Next, we look at the hundreds digit. Again, we need to find two digits that, when multiplied by 2, will result in a number that, when added to the carry (which is 1 in this case), will give us a number ending in "G". The only possible pair that satisfies this condition is 7 and 6, with the carry being 1. Let's assign 7 to "W" and 6 to "R".
8. Our equation now becomes 76050 + 76050 = 1IG0T.
9. Finally, we come to the thousands digit. To determine the value for the letter "I", we need to find a digit that, when multiplied by 2, will result in a number that, when added to the carry (which is 1 in this case), will give us a number ending in "R". The only possible digit is 4. Therefore, we assign 4 to "I".
10. The complete equation is 76050 + 76050 = 14605T.
By following these steps, we have found a solution where the sum of two instances of "WRONG" equals "RIGHT" when each different letter in the addition problem is replaced with a different digit, with the constraint that "O" represents zero.