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School Lockers


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Newton Middle School has a hall with 500 lockers, all of which are closed. Five hundred students start down the hall. The first student opens every locker. The second student closes all the lockers that are multiples of 2. The third student changes (closes an open locker or opens a closed one) all multiples of 3. The fourth student changes all multiples of 4. And so on. After all students have finished with the lockers, how many lockers will be open?

February 28, 2005
Past Problems  
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E-mail Solutions to: pow@umassd.edu

   
  Correct Solutions 
 
  1. Radu Casian Ionescu. Montreal, Quebec, Canada
  2. Julie Sperfslage. Nemaha Valley Junior High, Seneca, KS
  3. Patrick McHenry. Gloucester City Schools
  4. Mike Osterfoss. Colorado School of Mines, Golden, CO
  5. Nathan Gould. Scarsdale High School, Scarsdale, NY
  6. Emily Stallbaumer. Nemaha Valley Junior High, Seneca,KS
  7. Matt Deters. Nemaha Valley Junior High, Seneca, KS
  8. Phillip Ai. Warnsdorfer Elementary School, East Brunswick, NJ
  9. Katie Kramer. Nemaha Valley Junior High, Seneca, KS
  10. James Endicott.  Good Counsel High School, Wheaton, MD
  11. Evan Durant. Dartmouth High School, Dartmouth, MA
  12. Kirill Korsak. Harper Park Middle School, Leesburg, VA
  13. Lutfi Latif. Walnut Creek, CA
  14. Aristides Kyriakakais.  Thessaloniki,  Greece
  15. Tim Poe. Austin, Texas
  16. Sahana Vasudevan.  Country Parkway Elementary  School, Williamsville, NY
  17. Frank McGartland. Saskatoon, SK., Canada
  18. Josh Rasera. Southridge School, Surrey, BC, Canada
  19. Aquil Virani. Southridge Senior School, Surrey, BC, Canada
  20. Roland Vyncke. Brugge, Belgium
  21. Jason Tripp. Westside High School, Macon, GA
  22. Hamilton Hardison. University of Georgia. Athens, GA
  23. Adrian Atanasiu. Bucharest University, Romania
  24. Dennis Muniz. Commack, NY
  25. Thomas Woodward.
  26. Cheryl Dalinghaus. Nemaha Valley Junior High, Seneca, KS
  27. Kaitlin Nolte. Nemaha Valley Junior High, Seneca, KS
  28. Matthew. Fangman Nemaha Valley Junior High, Seneca, KS
  29. Teruo Goto. Aichi, Japan
  30. Sid Panjabi. Harmon Middle School, Aurora, OH
  31. Christine Chen. South Pasadena Middle School, South Pasadena, CA
  32. Cindy Sung. Duchesne Academy, Houston, TX
  33. Lusha Zhou. Richmond Secondary, Richmond, BC, CA
  34. David Shi. Jls Middle School, Palo Alto, CA
  35. Juan Ortega Suárez. ITESM Campus Central de Veracruz, Mexico
  36. Crystal Koo. Steveston Secondary School, Richmond, B.C., Canada
  37. Jerome Cherry. NAIT, Edmonton, Alberta, Canada
  38. Ken Duisenberg. Roseville, CA
  39. Norman Peng. Lowell High School, San Francisco, CA
  40. Lana Ho. South Pasadena Middle School, South Pasadena, CA
  41. Mark Scott, Boston MA
  42. Cameron Saunders, Brookstone
  43. Caleb Jones, Brookstone School.
  44. David Friedman, Sippican Elementary School, Marion, MA
  45. Mitchell Donald. Southridge Schoole, Surrey, BC, Canada
  46. Mac Dillon. Brookstone school, Columbus, GA
  47. Kelsey Martin. SOuthridge School, BC, Canada
  48. Sam Coffin. Brookstone School, Columbus, GA
  49. Tina Wang. Ryan Middle School, Fresh Meadows, NY
  50. Ann Norman. Brookstone School, Columbus, GA
  51. Gaylord Focker. New York University, New York, NY
  52. Alex McIntire. Brookstone School Columbus, GA
  53. Paige Janke. Brookstone School, Columbus, GA
  54. Allamanis Miltiadis. Anatolia High School, Thessaloniki, Greece
  55. Sarah Chen. Marie Curie Middle School, Bayside, NY
  56. Jeanette Crawford.
  57. Blake Bowden. Brookstone School, Columbus, GA
  58. Sam Rosenberg. Monta Vista High School, Cupertino, CA
  59. Rebecca Crawford. Columbus, GA
  60. Danny Myers. Harmon Middle School, Aurora, OH
  61. Robert Bush. Columbus, GA
  62. Yifeng Qin, Deep Run High School, Richmond, VA
  63. Sally Pound. Columbus, GA
  64. Ali Wade. Brookstone School, Columbus, GA
  65. Crystal Church.
  66. Rodney Clingaman. Fishers, IN
  67. Peter Schaffer. Budapest University of Technology and Economics, Budapest, Hungary
  68. Anshuman Sahu. Mnnit, Allahabad, India
  69. Joshua Sanchez. Clemente High School, Chicago, IL
  70. Jackie Henson. Brookstone School, Columbus, GA
  71. Gerald Stenklyft. Bishop Kenny High School, Jacksonville, FL
  72. Lane White. Brookstone School Columbus, GA
  73. Warner Kennon. Brookstone School, Columbus, GA
  74. Matt West. South Pasadena Middle School, South Pasadena, CA
  75. Collier Trotter. Brookstone School, Columbus, GA
  76. Mr Cambra. Hastings Middle School, Fairhaven, MA
  77. Brian Hetrick. University of New Hampshire, Manchester NH
  78. SooIn Yoon. South Pasadena Middle School,South Pasadena, CA
  79. Kevin Kimberlin. Creekwood Middle School, Kingwood, TX
  80. Derek Aegerter.
  81. Ali Chavez. Creekwood Middle School, Kingwood, TX
  82. Omer Parlu. Yuzyil Isil Primary S, Istanbul, Turkey
  83. Kelly Johnson. Brookstone School, Columbus, GA
  84. Bar Gringrass.Lapid school, Hod Hasahron, Israel
  85. Jacqueline Pendleton. Creekwood Middle School, Kingwood, TX
  86. Shelby Hagberg. Creekwood Middle School, Kingwood, TX
    50% of respondents successfully answered this problem. 
   


 



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