Perfect Cubes






Perfect Cubes


A Cubic box contains 27 congruent large balls. Another cubic box the same size contains 64 congruent smaller balls. All 91 balls are made from the same material and have walls that are the same thickness. Each layer contains the same number of balls in each box but the number of balls in a layer of one box is not necessarily equal to the number of balls in a layer of the other. In both boxes, the outside balls on each layer touch the inside wall of the box containing them. Which box is heavier? State a conclusion about M and N balls where both M and N are perfect cubes.

Correct Solutions:


  1. Robin Campbell. Lake Highland Prep, Orlando, FL
  2. Candace Gillespie. Katella HS, Anaheim, CA
  3. Naomi Turner. The Mount School, York, England, UK
  4. Justin Lam. College Park HS, Pleasant Hill, CA
  5. Angel Lin. Whittier Christian HS, Whittier, CA
  6. Frank Kuo. Los Altos HS, Hacienda Heights, CA
  7. Mohammed Saadullah Habib. Oviedo HS, Oviedo, FL
  8. Ellen Edwards. Forest HS, Ocala, FL
  9. Erin Perkins. Lake Highland Prep, Orlando, FL
  10. Travis Stepan. Sauk Centre HS, Sauk Centre, MN
  11. Teddy Schaffer. The Westminster Schools, Atlanta, GA
  12. Angela Farrel. Sauk Centre HS, Sauk Centre, MN
  13. Kristen Butler. Forest HS, Ocala, FL
  14. Amin Gomos. Fourth Baptist Christian, Minneapolis MN
  15. Arthur Chang. Los Altos HS, Hacienda Heights, CA
  16. Brian Yang. Los Altos HS, Hacienda Heights, CA
  17. Becky Cheng. Los Altos HS, Hacienda Heights, CA
  18. Jack Lai. Los Altos HS, Hacienda Heights, CA
  19. Chris Martin. Oviedo HS, Oviedo, FL
  20. Chris Young. Center For Arts & Sciences, Saginaw, MI
  21. Sean Geary. Lake Highland Prep, Orlando, FL
  22. Patrick McHenry. Oviedo HS, Oviedo, FL
  23. Geoffrey Bakker. Rickards HS, Tallahassee, FL
  24. Angie Coombs. Oviedo HS, Oviedo, FL
  25. Darren Kwong. South Pasadena MS, South Pasadena, CA
  26. Vladimir Duchatelier. Forest HS, Ocala, FL
  27. John Martin. Colonial Heights HS, Colonial Heights, VA
  28. Richard Cheng. Los Altos HS, Hacienda Heights, CA
  29. Alex Lorbert. Yeshivah of Flatbush HS, Brooklyn, NY
  30. Daron Spektor. Brixner JHS, Klamath Falls, OR
  31. Koos van Zyl. Overkruin HS, Pretoria, South Africa
  32. Jessica Marshall. Oviedo HS, Oviedo, FL






Previous Problems