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

Answer 1

9641 + 9641 = 19282

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.