Problem:
Sally has five red cards numbered 1 through 5 and four blue cards numbered 3 through 6 . 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 R1, .., R5 and B3, ..., B6 denote the numbers on the red and blue cards, respectively. Note that R4 and R5 divide evenly into only B4 and B5, respectively. Thus the stack must be , or the reverse. Since divides evenly into only and , we must have , R5, or the reverse. Since R3 divides evenly into only B3 and B6, the stack must be R4, B4, R2, B6, R3, B3, R1, B5, R5, or the reverse. In either case, the sum of the middle three cards is .
The problems on this page are the property of the MAA's American Mathematics Competitions