Question

Each letter in this addition problem stands for a different digit, but, for example, all of the
H’s stand for the same digit. Reconstruct the problem to find the value of THERE.
HALT
+HALT
———-
THERE

1. MichaelMet
9641 + 9641 = 19282
Step-by-step explanation:
You want to assign a different digit to each of the letters H, A, L, T, E, R such that …
HALT + HALT = THERE

### Solution

The T in the most significant digit of the sum must be T = 1, because a carry from the sum of two digits cannot exceed 1. That means E = 2. In order for H+H = TH, we must have …
H + H + 1 = 10 + H
H = 9
In order for there to be a carry into the 4th column (from the right), the value of A must be 5 more than the value of T:
A = 6
Since E in the third sum digit is even, there can be no carry from the sum L +L = R. This leaves R an even digit not 0, 2, or 6. It cannot be 4, because that would require L=2, but we already have E=2. This leaves R = 8 and L = 4.
The sum is …
HALT +HALT = THERE   ⇒   9641 +9641 = 19282
The value of THERE is 19282.