School Lockers 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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	Correct Solutions
	Radu Casian Ionescu. Montreal, Quebec, Canada Julie Sperfslage. Nemaha Valley Junior High, Seneca, KS Patrick McHenry. Gloucester City Schools Mike Osterfoss. Colorado School of Mines, Golden, CO Nathan Gould. Scarsdale High School, Scarsdale, NY Emily Stallbaumer. Nemaha Valley Junior High, Seneca,KS Matt Deters. Nemaha Valley Junior High, Seneca, KS Phillip Ai. Warnsdorfer Elementary School, East Brunswick, NJ Katie Kramer. Nemaha Valley Junior High, Seneca, KS James Endicott.  Good Counsel High School, Wheaton, MD Evan Durant. Dartmouth High School, Dartmouth, MA Kirill Korsak. Harper Park Middle School, Leesburg, VA Lutfi Latif. Walnut Creek, CA Aristides Kyriakakais.  Thessaloniki,  Greece Tim Poe. Austin, Texas Sahana Vasudevan.  Country Parkway Elementary  School, Williamsville, NY Frank McGartland. Saskatoon, SK., Canada Josh Rasera. Southridge School, Surrey, BC, Canada Aquil Virani. Southridge Senior School, Surrey, BC, Canada Roland Vyncke. Brugge, Belgium Jason Tripp. Westside High School, Macon, GA Hamilton Hardison. University of Georgia. Athens, GA Adrian Atanasiu. Bucharest University, Romania Dennis Muniz. Commack, NY Thomas Woodward. Cheryl Dalinghaus. Nemaha Valley Junior High, Seneca, KS Kaitlin Nolte. Nemaha Valley Junior High, Seneca, KS Matthew. Fangman Nemaha Valley Junior High, Seneca, KS Teruo Goto. Aichi, Japan Sid Panjabi. Harmon Middle School, Aurora, OH Christine Chen. South Pasadena Middle School, South Pasadena, CA Cindy Sung. Duchesne Academy, Houston, TX Lusha Zhou. Richmond Secondary, Richmond, BC, CA David Shi. Jls Middle School, Palo Alto, CA Juan Ortega Suárez. ITESM Campus Central de Veracruz, Mexico Crystal Koo. Steveston Secondary School, Richmond, B.C., Canada Jerome Cherry. NAIT, Edmonton, Alberta, Canada Ken Duisenberg. Roseville, CA Norman Peng. Lowell High School, San Francisco, CA Lana Ho. South Pasadena Middle School, South Pasadena, CA Mark Scott, Boston MA Cameron Saunders, Brookstone Caleb Jones, Brookstone School. David Friedman, Sippican Elementary School, Marion, MA Mitchell Donald. Southridge Schoole, Surrey, BC, Canada Mac Dillon. Brookstone school, Columbus, GA Kelsey Martin. SOuthridge School, BC, Canada Sam Coffin. Brookstone School, Columbus, GA Tina Wang. Ryan Middle School, Fresh Meadows, NY Ann Norman. Brookstone School, Columbus, GA Gaylord Focker. New York University, New York, NY Alex McIntire. Brookstone School Columbus, GA Paige Janke. Brookstone School, Columbus, GA Allamanis Miltiadis. Anatolia High School, Thessaloniki, Greece Sarah Chen. Marie Curie Middle School, Bayside, NY Jeanette Crawford. Blake Bowden. Brookstone School, Columbus, GA Sam Rosenberg. Monta Vista High School, Cupertino, CA Rebecca Crawford. Columbus, GA Danny Myers. Harmon Middle School, Aurora, OH Robert Bush. Columbus, GA Yifeng Qin, Deep Run High School, Richmond, VA Sally Pound. Columbus, GA Ali Wade. Brookstone School, Columbus, GA Crystal Church. Rodney Clingaman. Fishers, IN Peter Schaffer. Budapest University of Technology and Economics, Budapest, Hungary Anshuman Sahu. Mnnit, Allahabad, India Joshua Sanchez. Clemente High School, Chicago, IL Jackie Henson. Brookstone School, Columbus, GA Gerald Stenklyft. Bishop Kenny High School, Jacksonville, FL Lane White. Brookstone School Columbus, GA Warner Kennon. Brookstone School, Columbus, GA Matt West. South Pasadena Middle School, South Pasadena, CA Collier Trotter. Brookstone School, Columbus, GA Mr Cambra. Hastings Middle School, Fairhaven, MA Brian Hetrick. University of New Hampshire, Manchester NH SooIn Yoon. South Pasadena Middle School,South Pasadena, CA Kevin Kimberlin. Creekwood Middle School, Kingwood, TX Derek Aegerter. Ali Chavez. Creekwood Middle School, Kingwood, TX Omer Parlu. Yuzyil Isil Primary S, Istanbul, Turkey Kelly Johnson. Brookstone School, Columbus, GA Bar Gringrass.Lapid school, Hod Hasahron, Israel Jacqueline Pendleton. Creekwood Middle School, Kingwood, TX Shelby Hagberg. Creekwood Middle School, Kingwood, TX
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 Last Updated On: 11/16/05