Problem:
Sally has five red cards numbered through and four blue cards numbered through . She stacks the cards so that the colors alternate and so that the number on each red card divides evenly into the number on each neighboring blue card. What is the sum of the numbers on the middle three cards?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let and denote the numbers on the red and blue cards, respectively. Note that and divide evenly into only and , respectively. Thus the stack must be , or the reverse. Since divides evenly into only and , we must have , or the reverse. Since divides evenly into only and , the stack must be , or the reverse. In either case, the sum of the middle three cards is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions