In the following problem, the digits 0-9 have been replaced with letters. Can you reconstruct the original multiplication problem by identifying what digit each letter represents?
TEA
(times)x_TEA_
SEA
TNNA
(add)t_TEA_
(ans.) CHINA
To solve this problem and reconstruct the original multiplication problem, we need to determine the correct digit for each letter. We can do this by analyzing the given information and working backwards step by step.
Let's start with the first step. We know that TEA multiplied by TEA gives us SEA. Since SEA ends in A, it means that T multiplied by T only yields a single-digit result ending in A. This implies that T must be either 1 or 6 (as the only two possibilities).
Next, let's look at the second step. From TNNA plus TEA equals CHINA, we can deduce that adding TEA to TNNA resulted in a carry-over to the next digit (N + A). The only way this can happen is if A itself is 1, resulting in a carry-over of 1.
Now, we have two possibilities left for T: 1 or 6. Let's consider T as 1 and continue.
In the first step, TEA multiplied by TEA would be 1EA multiplied by 1EA, which does not end in A. Therefore, T cannot be 1.
Now, we can conclude that T must be 6.
Using T = 6, we can reconstruct the original multiplication problem:
6EA
(times)x_6EA_
SEA
TNNA
(add)t_6EA_
(ans.) CHINA
We successfully determined the correct digit for each letter and reconstructed the original multiplication problem.