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number theory junior
Problem
If and are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is \begin{array}[t]{cccc} 9 & 8 & 7 & 6 \\ & A & 3 & 2 \\ & B & 1 \\ \hline \end{array}
(A)
(B)
(C)
(D)
Solution
The minimum possible value of this sum is when , which is The largest possible value of the sum is when , making the sum Since all the possible sums are between and , they must have digits.
Final answer
B