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The Ultimate Pyramid

A

 28

 496

 8128

33550336

8589869056

137438691328

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Determine the value of A that begins this pyramid of numbers and also provide your reasoning for determining this value.

December 5, 2005
Past Problems  
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E-mail Solutions to: pow@umassd.edu

   
  Correct Solutions 
 
  1. Jon Eisenberg. Dartmouth High School, Dartmouth MA
  2. Matt Kestenbaum. Dartmouth High School, Dartmouth, MA
  3. Francois Bonjean. Liege, Belgium
  4. Brian Hetrick. UNH, Manchester, NH
  5. Emil Lalov. Mathematical High School, Pleven, Bulgaria
  6. Lisa Schechner. Schreiber HS, Port Washington, NY
  7. Raphael Chalhub. Pan American School of Bahia, Salvador, Bahia, Brazil
  8. Gustavo Amorim. Pan American School of Bahia, Salvador, Bahia, Brazil
  9. Caroline Brander. Trinity High School, River Forest, IL
  10. Katie Grunow. Trinity High School, River Forest, IL
  11. Charles Keebaugh. Colorado Springs, CO
  12. Frank McGartland. Saskatoon, SK., Canada
  13. Thomas Robertson. Riverside, RI
  14. Genoa Warner. Dartmouth High School, Dartmouth, MA
  15. Sarah Maldonado. Creekwood Middle School, Kingwood, TX
  16. Amanda Tu. Southridge School, Surrey, BC, Canada
  17. Rohit Bollineni. Power Midle School, Farmington Hill, MI
  18. Sahit Bollineni. Highmeadow Common Campus, Farmington Hill, MI
  19. Jay Counts Ocala, FL
  20. Chris Oaks. Lower Merion High School
  21. Darren Brown. West Port High School, Ocala, FL
  22. John Jones Jr. Belleville East High School, Belleville, IL
  23. Carolyn Merchant. DHS, South Dartmouth, MA
  24. Maggie Schoening. Dartmouth High, Dartmouth, MA
  25. Max White. South Pasadena Middle School, South Pasadena, CA
  26. Rin Sone. South Pasadena Middle School, CA
  27. Phillip Ai.  Hammarskjold Middle School, East Brunswick, NJ
  28. Harry Siebert. Infineon, Munich, Germany
  29. Bar Greengrass. Israel
  30. Mrinal Singh. Kendriya Vidyalaya, H.V., Shillong, Meghalaya, India
  31. Kathrin Baur. Pan American School of Bahia, Salvador, Bahia, Brazil
  32. Raphael Leitz. Pan American School of Bahia, Salvador, Bahia, Brazil
  33. Jerrold Greenberg. New York, NY
  34. Craig Sidell. New York, NY
  35. Adrian Atanasiu. Bucharest, Romania
  36. Seana McKee. Dartmouth High School, Dartmouth, MA
  37. Ashvin Swaminathan. Harker Elementary School, San Jose, CA
  38. Abigail Finger. Dartmouth High School, Dartmouth, MA
  39. Maggie Schoening. Dartmouth High, Dartmouth, MA
  40. Jenna Custodio. Dartmouth High School, Dartmouth, MA
  41. David Shi. JLS MIddle School, Palo Alto, CA
  42. Rachel Bier. Dartmouth High, Dartmouth, MA
  43. Nancy Huynh.. MVRCS Upper School. Everett, MA
  44. Amanda DeCosta. Dartmouth High School, Dartmouth, MA
  45. Tom Wilcox, Math Instructor, Wilcox Technical H.S., Meriden, CT
  46. Wu Ken. Pan American School of Bahia, Brazil, Bahia, Salvador
  47. Brandon Simmons. Decatur Central High, Indianapolis, IN
  48. Bob Mitchell, Normal, IL
  49. Marius Damian. Braila, Romania
  50. Josh Gow. Sauk Centre HS, Sauk Centre, MN
  51. Brad Zoller, Decatur Central Highschool, Indianapolis, IN
  52. Peter Moynahan. Rye Junior High, Rye NH
  53. David Shi. JLS MIddle School, Palo ALto, CA
  54. Alan Scott. Elizabethtown High School, Elizabethtown, KY
  55. Sagar Patel. Brookstone School, Columbus, GA
  56. Daniel Pyon. South Pasadena Middle School, South Pasadena, CA
  57. Brianna Loo. South Pasadena Middle School, South Pasadena, CA
  58. Kevin Temew. Davao Christian High School, Davao City, Philippines
  59. Chris Hanes. West Port High School,Ocala, FL
  60. Amy Skidmore.  John Hardin High School, Elizabethtown, KY
  61. Tim Poe. Austin, TX
  62. Emily Cowperthwaite. Leo Hayes High School, Fredericton, NB, Canada
  63. Nicholas Caligaris. Brookstone School, Columbus, GA
  64. Anil Nataraj. Brookstone School, Columbus, GA
  65. Aashrita Mangu. South Pasadena Middle School, South Pasadena, CA USA
  66. Michelle Lam. South Pasadena Middle School, South Pasadena, CA
  67. Niels Nielsen. Denmark
  68. Carter Galbraith. Brookstone School, Columbus, GA
  69. Kelly Temew. Davao Christian High School, Davao City, Philippines
  70. Ken Sagynbekov. Bishkek, Kyrgyz Republic
  71. Karina Shaw. Laguna Beach High School, CA
  72. Curtis Schneider. Winnipeg, Manitoba, Canada
  73. Dalia McGlone. Charleston, SC
  74. Nikki Tan. Southridge, Surrey BC, Canada
  75. Matthew Wong. South Pasadena, South Pasadena Middle School, CA
  76. Jenna Kirk. Oak Park River Forest High School, Oak Park, IL
  77. Nibal Nsr. West Bloomfield High School, West Bloomfield, MI
  78. Sheyi Alamou. International School of Uganda, Uganda, Africa
  79. Evan Case. Freetown Lakeville Middle School, Lakeville, MA
  80. Cassie Smith. Freetown Lakeville Middle School, Lakeville, MA
  81. Evan Field. Freetown Lakeville Middle School, Assonet, MA
  82. Allamanis Miltiadis. Anatolia High School, Thessaloniki, Greece
  48% of respondents successfully answered this problem.


 



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