Let $A3BC$ and $DE2F$ be four-digit numbers where each letter represents a different digit greater than 3.…
Let $A3BC$ and $DE2F$ be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of $A$ and $D$?
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Solution
Each letter is a distinct digit greater than 3, i.e. from {4,5,6,7,8,9}. The sum $A3BC + DE2F = 15902$. Analysing the column additions with carries, the thousands digits A and D (with carry) sum to 15, giving $A + D = 15$ with valid distinct digits such as A=6, D=9. The difference between the values of A and D is 3.