Tower of Power






Tower of Power


5^5^5 means 5^(5^5) or 5^3125 and could be called a "tower" of powers. Suppose you had the tower 5^5^5^...^5 done 999,000 times. What is the remainder when this number is divided by 7?

Correct Solutions:


  1. Huan Vo. Collins Hill HS, Suwanee, GA
  2. Morgan Chen. Mt. Carmel HS, San Diego, CA
  3. Robin Donelson. Boise HS, Boise, ID
  4. Batman. Swami Vivekanand HS, Chembur, Mumbai, India
  5. Alex Lorbert. Yeshivah of Flatbush HS, Brooklyn, NY
  6. Tim Borgmann. Sauk Centre HS, Sauk Centre, MN
  7. Nasser S. Demir. American School of Kuwait, Kuwait
  8. Joel Merritt. Merritt Homeschool, Lutz, FL
  9. Greg Whisenant. Buchanan ES, Pierre, South Dakota
  10. Katya Permiakova. Lisgar Collegiate Institute, Ottawa, ON, Canada
  11. Sorin Ionescu. Ecole Secondaire Dorval, Dorval, Quebec, Canada
  12. Ashlea Fadem. Lake Highland Prep, Orlando, FL
  13. Adam Maberry. Buchanan ES, Pierre, SD
  14. Wojciech Lewkowicz. Lemont HS, Lemont, IL
  15. Puja Guha. American School of Kuwait, Kuwait
  16. Tao Tao Chen. Ellis ES, Sunnyvale, CA
  17. Kathleen Lysaught. Mannheim HS, Mannheim, Germany
  18. Justin Lam. College Park HS, Pleasant Hill, CA
  19. Michael Moyer. The Way Home School, Carlisle, PA
  20. Christopher Rice. C.E. Byrd HS, Shreveport, LA
  21. Christine LaPointe. Marathon HS, Marathon, FL
  22. Isaac Dooley. Vestavia Hills HS, Vestavia Hills, AL
  23. Angela Ryder. C.E. Byrd HS, Shreveport, LA
  24. Kenley Stringer. Rickards HS, Tallahassee, FL
  25. Eric Madsen. Rickards HS, Tallahassee, FL
  26. Shereen Kassam. Lake Highland Prep, Orlando, FL
  27. Blake Hodgin. Moscow HS, Moscow, ID
  28. Ming De Lin. Fair Lawn HS, Fair Lawn, NJ
  29. Aly Merchant. Woburn Collegiate Institute,Toronto, ON, Canada