The figure below depicts the fifteen balls racked up for a game of pool. The balls are numbered from 1 to 15. You must determine the placement of the balls so that the following property is true:
The value of every ball in the bottom four rows is the difference between the values of the two balls immediately above it. Balls 1, 2, and 3 have been positioned for you.


 

Solution to the Problem:



Correctly solved by:

1. Akash Patel Columbus, Georgia
2. Misty Carlisle Winchester, Virginia
3. John Funk Ventura, California
4. Bill Funk San Antonio, Texas
5. Richard Johnson La Jolla, California
6. Andrew Marvets Columbus, Georgia
7. Franklin Harcourt Columbus, Georgia
8. Keith Mealy Cincinnati, Ohio
9. Jeffrey Gaither Winchester, Virginia
10. Victor Larsson, Simon Palmquist, Adam Hillerbrand-Rune Tullängsskolan Sweden
11. Nina Karlsson Örebro, Tullängsskolan, Sweden
12. Emelie Peippo and Kajsa Axin Tullängsskolan, Örebro, Sweden
13. Martin Dahl, Frida Öijerholm and Joakim Dahlstedt Tullängsskolan, Örebro, Sweden
14. Ali Alatabi Tullängskolan, Örebro, Sweden
15. Kathryn Harris Winchester, Virginia
16. Samantha Stockdall Corder, Missouri
17. Dave Smith Toledo, Ohio
18. Kristofer Friman Tullängsskolan, Sweden
19. Viktor Bergqvist Tullängen, Sweden
20. David Sundelius Tullängsskolan, Örebro, Sweden
21. James Alarie University of Michigan -- Flint
Flint, Michigan
22. Ms. Bearse's Grade 9 class Ontario, Canada
23. David Wong Winchester, Virginia
24. Britney Ford Winchester, Virginia
25. Jason Aikens Stephens City, Virginia
26. Larry Schwartz Trumbull, Connecticut
27. Martha Johnston Columbus, Georgia
28. Suk Lim Woodbridge, Virginia
29. Frank Sitarski Plainville, Massachusetts
30. Walt Arrison Philadelphia, Pennsylvania
31. Nate Wilson Winchester, Virginia
32. Andrew Oliver Winchester, Virginia
33. Anne Beavers Arlington, Virginia
34. Joanna Monhollen Winchester, Virginia
35. Irene Mathieu Winchester, Virginia