Posted by Amy on .
John is passing out RED, WHITE, and BLUE construction paper for an art project. There are (12) people in his group. John, who likes to show off, tells everyone to watch closely as he hands out the paper. The first person gets a RED paper. John puts the second paper at the bottom of the stack. John gives the second person a WHITE paper. John puts the fourth paper at the bottom of the stack and gives the third person a BLUE paper. John continues this pattern until there is no more paper. How did he have to stack the colored paper so that he could pass it out this way. (Thank you for any help this has stumped me for hours)

Math 
MathMate,
Here's how he distributed the papers. The vertical bar separates the paper that have been distributed and those remaining.
The last line shows the papers in the original order which was distributed.
All we need to do is to put in the desired order of colours, RED, WHITE and BLUE.
1 2 3 4 5 6 7 8 9 10 11 12
1  3 4 5 6 7 8 9 10 11 12 2
1 3  5 6 7 8 9 10 11 12 2 4
1 3 5  7 8 9 10 11 12 2 4 6
1 3 5 7  9 10 11 12 2 4 6 8
1 3 5 7 9  11 12 2 4 6 8 10
1 3 5 7 9 11  2 4 6 8 10 12
1 3 5 7 9 11 2  6 8 10 12 4
1 3 5 7 9 11 2 6  10 12 4 8
1 3 5 7 9 11 2 6 10 4  8 10
1 3 5 7 9 11 2 6 10 4 8  10
1 3 5 7 9 11 2 6 10 4 8 10
1=RED
3=WHITE
5=BLUE
7=RED
9=WHITE
11=BLUE
2=RED
6=WHITE
...