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number theory junior
Problem
When placing each of the digits in exactly one of the boxes of this subtraction problem, what is the smallest difference that is possible? \begin{array}[t]{cccc} & \boxed{} & \boxed{} & \boxed{} \\ - & & \boxed{} & \boxed{} \\ \hline \end{array}
(A)
(B)
(C)
(D)
Solution
When trying to minimize , we minimize and maximize . Since in this problem, is three digit and is two digit, we set and . Their difference is .
Final answer
C