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?

From: MAA Minute Math

R5 B5 R1 B3 R3 B6 R2 B4 R4

Therefore: 12

This one wasn’t too difficult. Since we are dividing the constraining blue cars are your prime numbers. Therefore 3 and 5, since you only have one 1 card your 3 and 5 have to both use it. Then since they are prime, your red 3 and 5 go on the other side of the blues. From there, the next 4 cards fall into place. You’d have to have a 10 to put anything next to red 5 so you the 4 other cards go on that side of the stack.

(I hope your readers don’t mind me answering these like I have been.)

Also, what about the solution to #2? Aren’t you getting ahead of yourself?