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1998 CEMC Gauss (Grade 7) Problems/Problem 16

Problem

Each of the digits 3, 5, 6, 7, and 8 is placed one to a box in the diagram. If the two digit number is subtracted from the three digit number, what is the smallest difference?

[Align three boxes to the right and two boxes below so it looks like a three digit number subtracting a two digit number.]

$\text{(A)}\ 269 \qquad \text{(B)}\ 278 \qquad \text{(C)}\ 484 \qquad \text{(D)}\ 271 \qquad \text{(E)}\ 261$

Solution

Make the 3-digit number as small as possible (356) and the 2-digit number as large as possible (87). The smallest difference is $\boxed{\text{(A)} \quad 269.}$

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