![15TH ANNUAL HARVARD-MIT MATHEMATICS TOURNAMENT, 11 FEBRUARY 2012 GUTS ROUND 21. [131 Let N be a three-digit integer such that the difference between any two positive integer factors of N is divisible by 3. Let d(N) denote the number of positive integers which divide N. Find the maximum possible value of N d(N) 22. 13] For each positive integer n, there is a circle around the origin with radius n. Rainbow Dash starts off somewhere on the plane, but not on a circle. She takes off in some direction in a straight path. She moves 5 units before crossing a circle, then v5 units, then 36 units. What distance will she travel before she crosses another circle? 23. 13] Points X and Y are inside a unit square. The score of a vertex of the square is the minimum distance from that vertex to X or Y. What is the minimum possible sum of the scores of the vertices of the square? 24. [13] Franklin has four bags, numbered 1 through 4. Initially, the first bag contains fifteen balls, numbered 1 through 15, and the other bags are empty. Franklin randomly pulls a pair of balls out of the first bag, throws away the ball with the lower number, and moves the ball with the higher number into the second bag. He does this until there is only one ball left in the first bag. He then repeats this process in the second and third bag until there is exactly one ball in each bag. What is the probability that ball 14 is in one of the bags at the end?](https://i.kym-cdn.com/photos/images/original/000/265/720/136.jpg "136.jpg")
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Image #265,720
Uploaded by Platus Mar 10, 2012 at 11:37AM EST
Origin Entry: My Little Pony: Friendship is Magic
File type: jpg
Resolution: (720px x 540px)
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Uploaded by Platus Mar 10, 2012 at 11:37AM EST
Origin Entry: My Little Pony: Friendship is Magic
File type: jpg
Resolution: (720px x 540px)
File size: 88.2 KB
