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?
Choose the correct choice from the following:
A) 8	B) 9	C) 10	D) 11	E) 12
The cards are stacked so that the colors alternate: R-B-R-B-R-B-R-B-R.   We are also told that the number on each red card divides evenly into the number on each neighboring blue card.   There are two primes in Blue cards: 3 and 5. Their divisors are 1 and 3 AND 1 and 5, respectively. Thus R1 must be between R3 and R5, R3 must be by B3 and R5 must be by B5: 3-3-1-5-5.   Next, add multiple of 3 to the left of 3: 6-3-3-1-5-5.   Add factor of 6 to the left of 6: 2-6-3-3-1-5-5.   Add multiple of 2 to the left of 2: 4-2-6-3-3-1-5-5.   And finally add factor of 4 to the left of 4: 4-4-2-6-3-3-1-5-5.   The sum of the numbers on the middle three cards is  6+3+3= 
<gadget id="calculator"> 6+3+3</gadget>
<output>12</output>
12.   Answer: 12.
<result>E</result>
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?