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Next Row

1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
1 3 1 1 2 2 2 1

Determine the next row of numbers in the above pattern of whole numbers.  Good luck.  You might need to say these numbers to yourself.

October 10, 2005
Past Problems  
pencil

E-mail Solutions to: pow@umassd.edu

   
  Correct Solutions 
 
  1. Adrian Atanasiu. Bucharest, Romania
  2. Harry Siebert. Infineon, Munich, Germany
  3. Roland Vyncke, Brugge, Belgium
  4. Bob Mitchell. Normal, IL
  5. Radu Ionescu. Montreal, Quebec, Canada
  6. Juan Ortega. ITESM, CCV, Mexico
  7. Aristides Kyriakakis.  Thessaloniki.  Greece
  8. Lisa Schechner. Schreiber HS, Port Washington, NY
  9. Michael Chlebowski. Markham District High School. Markham, Ontario
  10. Genoa Warner. Dartmouth High School, Dartmouth, MA
  11. Raphael Chalhub. Pan American School of Bahia, Salvador, Bahia, Brazil
  12. Pedro Teixeira. Pan American School of Bahia, Salvador, Bahia, Brazil
  13. Gustavo Amorim. Pan American School of Bahia, Salvador, Bahia, Brasil
  14. Caio Foneca. Pan American School of Bahia, Salvador, Bahia, Brasil
  15. Michael Schmatz. Pan American School of Bahia, Salvador, Bahia, Brazil
  16. Emil Lalov. Mathematical High School, Pleven, Bulgaria
  17. Andrew Sailor. Osceola Middle School, Ocala, FL
  18. Phillip Ai.  Hammarskjold Middle School, East Brunswick, NJ
  19. Jon Lewis. UNB, Fredericton, New Brunswick, Canada
  20. Mansi Raythatha. Creekwood Middle School, Kingwood, TX
  21. Harrison Jones. Blackmon Middle School, Columbus, GA
  22. Kathrin Baur. Pan American School of Bahia, Salvador, Bahia, Brazil
  23. Steigen Johnson. Pan American School of Bahia, Salvador, Bahia, Brazil
  24. Rufus Hallam. Canterbury, England
  25. Raphael Leitz. Pan American School of Bahia, Salvador, Bahia, Brazil
  26. Sarah Chen. Marie Curie Middle School, New York, NY
  27. Hamilton Hardison. University of Georgia, Athens, GA
  28. Jennifer Sailor. Osceola Middle School, Ocala, FL
  29. Sagar Patel. Brookstone School, Columbus, GA
  30. Dave Barron.  Chelmsford High School, Chelmford, MA
  31. Michael Fang. Osceola Middle School, Ocala FL
  32. Jon Satko, Porterville, CA
  33. Rachel Bier.  Dartmouth High, MA
  34. Pascale Philpot. Valencia Community College, Kissimmee, FL
  35. Nikki Tan. Southridge, Surrey,BC Canada
  36. Michael Schra. Merritt Island High School, Merritt Island, FL
  37. Jerrold Greenberg, New York, NY
  38. Annabel Otero, VCC, Kissimmee, FL
  39. Anna Li. Sandburg Middle School, Anoka, MN
  40. Alan Leung. Mississippi School for Mathematics and Science, Columbus, MS
  41. Tauseef Anam. Lakeview Academy, Gainesville, GA
  42. Chris Gatti. Lakeview Academy, Gainesville, GA
  43. Matthew Kestenbaum. Dartmouth H.S, Dartmouth, MA
  44. Daniel Macintyre, OFallon, IL
  45. Gabriele Mocci, Roma, Italy
  46. Jon Eisenberg. Dartmouth High School, Dartmouth, MA
  47. Meagan Cole. Lakeview Academy, Gainesville, GA
  48. Tim Poe. Austin, TX
  49. Peter Moynahan. Rye Junior High, Rye, NH
  50. Kelsey Abrams. Rye Junior High School, Rye, NH
  51. Jenna Osberg. Rye, NH
  52. Anna Genestreti.Rye Junior High, Rye, NH
  53. John Song. White Station High School, Memphis, TN
  54. Gavin Tse. South Pasadena Middle School, South Pasadena CA
  55. George Hatzikiriakos. Southridge School, Surrey, BC
  56. Maggie Schoening. Dartmouth High School, Dartmouth, MA
  57. Carolyn Merchant. Dartmouth High School, South Dartmouth, MA
  58. John Povilaitis. Rye Junior High School, Rye, NH
  59. Matthew Wong. South Pasadena Middle School, South Pasadena, CA
  60. Hannah Szynal. Dartmouth High School, Dartmouth, MA
  61. Courtney Potter. Creekwood Middle School, Kingwood, TX
  62. Olivia McGlone. Dartmouth, MA
  63. Tanvi Rastogi. Bridgewater-Raritan High School, Bridgewater, NJ
  64. Annelise Broussard. Creekwood Middle School. Kingwood, TX
  65. Dan Dietz. Creekwood Middle School, Kingwood, TX
  66. Alstyne Gravlee. St. Luke Middle School. Columbus, GA
  67. Neacsu Adrian. Pitesti, Romania
  68. Marius Damian. Braila, Romania
  69. Julie Strang. Valencia Community College, Kissimmee, FL
  70. Virginia Cornelius. Lafayette High School, Ocford, MS
  71. Karina Shaw. Laguna Beach High School, Newport Beach, CA
  72. Katherine X. Wang. South Pasadena Middle School, South Pasadena, CA
  73. Tiffany Chen. South Pasadena Middle School, CA
  74. Seana McKee. Dartmouth High School, Dartmouth, MA
  75. Wu John Ken. Pan American School of Bahia, Salvador, Bahia, Brazil
  76. Blakeley Coull. St.Luke School
  77. Betsy Price. Asheville Christian Academy, Asheville, NC
  78. Cray Math Project. New Castle, PA
  79. Max White. South Pasadena Middle School, South Pasadena, CA
  80. Brandon Torok. Carwise Middle School, Palm Harbor, FL
  81. Haley Lewandowski. Fern Hill Elementary School, West Chester, PA
  82. Albert Zhou.  Scott Middle School, Lincoln, NE
  83. Amanda Tu. Southridge School, Surrey, BC
  84. Dave P. International School of Uganda
  85. Brian Hetrick. UNH, Manchester NH
  86. Avi Dhaliwal. Southridge Secondary School, British Columbia, Canada
  87. Florian Jonker. Southridge School, Surrey, British Columbia, Canada
  88. John Lee. Southridge School. Surrey, BC Canada
  89. Katherine Steede. The Berkeley Institute, Bermuda
  90. Sarah Maldonado. Creekwood Middle School, Kingwood, TX
  91. John Segura. Dartmouth High School, South Dartmouth, MA
  92. Katie Cornnell. Carwise Middle Palm Harbor, FL
  93. Ce-Ce Fowler. Webster High School, Tulsa, OK
  94. Lorna Ferguson. Chelmsford High school
  95. Vincent Dang. Stanton College Preparatory School, Jacksonville, FL
  96. Shengzhi Li. Shrewsbury High School, Shrewsbury, MA
  97. Jerome Pierce. Brookstone School, Columbus, GA
  98. QSi Tran. Crane School, Santa Barbara, CA
  99. DeeDee Walker. St. Cloud, FL
  100. Wend Zeng, White Station High, Memphis, TN
  101. Larry Shiller. Wilton, CT
  102. James Kawakami.  South Pasadena, CA
  103. Scott Kawakami.  South Pasadena, CA
  104. Mary Middlebrook. Valencia Community College, Kissimmee, FL
  105. Brianna Loo. South Pasadena Middle School. South Pasadena, CA
  106. Kelsey Smith. Clinton Junior High, Clinton, AR
  107. Danny Gordon. Columbus, GA
  108. Leah Pendleton. Carwise Middle, Palm Harbor, FL
  109. Michelle Fitzgerald. Clinton Junior High, Clinton, AR\
  110. Matthew Capron. Troy, NY
  111. Kavika Daga. JFK High School, Iselin, NJ
  112. Raj Patel. Carwise Middle Schoool, Palm Harbor, FL
  113. Chiraag Gupta. Southridge School, South Surrey, BC, Canada
  114. Linda Liu. Parkview High School, Lilburn, GA
  115. Nathan Caldwell. Delaura Middle School, Satellite Beach, FL
  116. Ruth Douvres. Valencia Community College, Kissimmee, FL
  117. Aashrita Mangu. South Pasadena Middle School, Pasadena, CA
  118. Ryan Elmer. Creekwood Middle School, Kingwood, TX
  119. Adria Leduc. Southridge School, Surrey, BC
  120. Dianne Pflanz. VCC, Orlando, FL
  121. Minray Yang, Carwise Middle School
  122. Kelly Galvin. Rye Jounior High School, Rye, NH
  123. Gina Cruz. Kissimmee, FL
  124. Ishwantie Braun. Valencia Community College, Kissimmee FL
  125. Shura Watson. VCC, Kissimmee, FL
  126. Sarah Bartley. Rye Junior High School, Rye, NH
  127. Seong Ho Lee. Saigon South International School, Ho Chi Minh City, Vietnam
  128. Sheri Higgins. Valencia Community College, St. Cloud, FL
  129. Mary Smith. Valencia Community College, Kissimmee, FL
  37% of respondents successfully answered this problem.


 



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