The University of Mississippi
Math Contest

Problem of the Week

How Many Triples? - November 09, 2009

How Many Triples? Image

Let a, b, and c represent a triple of three consecutive integers {a, b, c}.  How many different triples exist such that the product of the three integers equals the sum of the integers? You must also provide each such triple.

 

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40% of the submitted answers were correct. (349 out of 878)
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Correct answers have been submitted by:

  1. Felix Rubinsteinf. Yroni Yod Dalet, Tel Aviv, Israel
  2. Cesar Santil. Uasd University, Santo Domingo, Dominican Republic
  3. Yuliya Nesterova. Queen's University, Ottawa, Canada
  4. Tom Stack. , Phoenix, AZ USA
  5. Dale Heffernan. Artist, San Rafael, CA USA
  6. Wenlin Fan. N/A, Moorestown, NJ USA
  7. Farid Lian. Atlantic University, Barranquilla, Colombia
  8. Stephen Ng. Hong Kong International School, Hong Kong, Hong Kong
  9. Janson Ng. Singapore International School, Hong Kong, Hong Kong
  10. Andrew Mowery. Mayde Creek, Katy, TX USA
  11. Frank McGartland. Retired, Saskatoon, Canada
  12. Corin Peterson. Columbus High School, Columbus, GA USA
  13. Gary Bremer. Na, Virginia Beach, VA USA
  14. Sun Woo Lee. St. Andrews School, Singapore, Singapore
  15. Chris Evert. , Sugar Land, TX USA
  16. Mihir Singhal. Walter Hays Elementary School, Palo Alto, CA USA
  17. Don Miller. retired, Oregon City, OR USA
  18. Chris Adkisson. Eku, Somerset, KY USA
  19. John Snyder. None, Oconomowoc, WI USA
  20. Garima Kapila. Fremont High School, Sunnyvale, CA USA
  21. Allison Mann. Chelmsford High School, Chelmsford, MA USA
  22. Graham Anderson. Christian Outreach College, Toowoomba, Australia
  23. Robert Bishop. Ubc Grad, Surrey, Bc, Canada
  24. Janet Nguyen. North Surrey, Surrey, Canada
  25. Roger Sheu. San Marino High School, San Marino, CA USA
  26. Taek Jin Kim. ABC International School, 10L, Ho Chi Minh City, Vietnam
  27. Rahul Sushil. School, Dhahran, Saudi Arabia
  28. Nabiel Hilmy Abuyazid. Dhahran School, Dhahran, Saudi Arabia
  29. Jaime Liew. Mercedes College, Adelaide, Australia
  30. Frans Janssen. Nijmegen, Netherlands
  31. Andrew Xu. Lowell High School, San Francisco, CA USA
  32. Rishi Kant Brahmpuria. Maulana Azad National Institute Of Technology, Bhopal, India
  33. Peter Lindgren. Slotte, Ljusdal, Sweden
  34. Young Joo Park. Student, Seoul, Korea (south)
  35. Anneleen Van Geenhoven. Ua, Antwerp, Belgium
  36. Dani Chavez. Creekwood Middle School!, Kingwood, TX USA
  37. Alan Drayton. International School Manila, Manila, Philippines
  38. Stephen Bidwell. Bridge Creek Elementary, Elgin, SC USA
  39. Ed Wilson. Eku, Richmond, KY USA
  40. Graham Gilbert. Retired Teacher, Haddon Hts, NJ USA
  41. Rakesh M. Business, New Delhi, India
  42. Kendrick Wong. Nus High School, Singapore, Singapore
  43. Mike Schieffer. None, Austin, TX USA
  44. Evamgelos Kyriakidis. Ntua, Athens, Greece
  45. Thomas Newsome. Weaver Academy, Greensboro, NC USA
  46. E. Rives. Uahuntsville, Huntsville, AL USA
  47. Janet Yang. N/a, Ridgewood, NJ USA
  48. Joe Neumann. Washington Township High School, Sewell, NJ USA
  49. Michael Strezebonski. Lincoln Trail, Mahomet, IL USA
  50. Chuanqi Shen. Raffles Institution, Singapore, Singapore
  51. Cody Woosoncroft. Northeast High School, Pasadena, MD USA
  52. Jim Hart. Coastal Carolina Community College, Jacksonville, NC USA
  53. Filip Goldefus. Brno University Of Technology, Brno, Czech Republic
  54. Yung-kuang Wang. Guangfu Junior High School, Taipei, Taiwan
  55. Gary Brensike. Saic, Germantown, MD USA
  56. Fengyuan Zhou. Hon.w.c.kennedy.c.i, Windsor, Canada
  57. Richard Ethier. Hon.w.c. Kenndy Ci., Windsor, Canada
  58. Maura Mackenzie. Berkshire, Sheffield, MA USA
  59. Edward Freeman. Uconn, West Hartford, CT USA
  60. Jon Scheck. N/A, New York, NY USA
  61. Shikhar Maheshwari. Bi, Mumbai, Mumbai, India
  62. Michael Coon. Niobrara County High School, Lusk, WY USA
  63. Sam Wright. Chelmsford High School, Chelmsford, MA USA
  64. Basil Kilisav. Qvi, Rochester, NY USA
  65. Bob Mitchell. None, Normal, IL USA
  66. Jelios Roytman. Ps 158, New York, NY USA
  67. Emily Dougelus. Bryan High, Bryan, TX USA
  68. Eugene Roytman. ., New York, NY USA
  69. Dan Brandt. Rga, St. Louis, MO USA
  70. Jonathan Foster. N/A, Sacramento, CA USA
  71. Gerald Queenan. Retired, Pawtucket, RI USA
  72. Graham Adams. Homeschool, Hoschton, GA USA
  73. Daniel (bobby) Newkirk. Lakeside Highschool, Martinez, GA USA
  74. Alan Best. Midtown, New York, NY USA
  75. Bobby Jordan. Lakeside High School, Martinez, GA USA
  76. Connie Chen. Amador Valley High School, Pleasanton, CA USA
  77. Cheryl Hampel. St. Marys Magnet Academy, Columbus, GA USA
  78. Mark Enderich. Wayne State University, Plymouth, MI USA
  79. Pat Costello. Eku, Richmond, KY USA
  80. Sergio Leonardi. -, Pearland, TX USA
  81. Gordon Bockus. Wilburton High School, Wilburton, OK USA
  82. Alan Moroz. Hon. W.c. Kennedy C.i., Windsor, On, Canada
  83. Zack Manasco. Niobrara County High School, Lusk, WY USA
  84. Bobby Markey. E.c. Glass High School, Lynchburg, VA USA
  85. Tent Eddies. Self-employed, Casselberry, FL USA
  86. John Macauda. Madison Middle, Trumbull, CT USA
  87. Brad Woods. N/A, Stonewall, Canada
  88. Meera Gopal. Business, Bridgewater, NJ USA
  89. Meera Kumar. Business, Bridgewater, NJ USA
  90. Meera Kumar. Business, Bridgewater, NJ USA
  91. Kristopher Skotek. Columbus School, Carteret, NJ USA
  92. Daniel Lopez Aguayo. Mathematics, Puebla, Mexico
  93. Armand Bajrami. Kennedy Collegiate Institute Highschool, Windsor, Canada
  94. Henri Zheku. Hon. W.c. Kennedy Collegiate Institute, Windsor, Canada
  95. David Zeng. Stuyvesant, Brooklyn, NY USA
  96. Kalpana Vijayakumar. Business, Bridgewater, NJ USA
  97. Jake Spivey. Niobrara County High School, Lusk, WY USA
  98. L. Zhou. Middle, Parsippany, NJ USA
  99. Hoa Tang. C.p.allen, Bedford, Canada
  100. Richard Wile. Charles P. Allen High School, Bedford, Nova Scotia, Canada
  101. Feng Shi. Shen Pan Zhe, Shenzhen, China
  102. Joe Cochran. Landmark Christian School, Fayetteville, GA USA
  103. Douglas Hauser. Biomedical Research At Usc, Los Angeles, CA USA
  104. Shaun Lising. Cherry Hill West High School, Cherry Hill, USA
  105. Qc Marniche. Cherry Hill West, Cherry Hill, NJ USA
  106. Robert Karch. N/a, Greenwich, CT USA
  107. Neha Kumar. Sms, Memphis, TN USA
  108. Tomas Farmer. Southridge School, Vancouver, DC Canada
  109. Bemjamin Hsu. Gloucester High School, Ottawa, Canada
  110. Max Li. Gloucester High School, Ottawa, Canada
  111. Paula A.. Gloucester High School, Ottawa, Canada
  112. Lily Loo. Kennesaw, Columbus, GA USA
  113. Vernick Bashi. Walled Lake Northern High School, Commerce Township, MI USA
  114. Rosa Paulina Anajao. University Of Santo Tomas, Quezon City, Philippines
  115. Angel Stoychev. Aprilov National High School, Gabrovo, Bulgaria
  116. Rui Guo. Na, Lawrence, KS USA
  117. Martina Bray. Eastern Kentucky University, Manchester, KY USA
  118. Akhil Enjety. Hon.w.ckennedy C.i, Windsor, Canada
  119. Kishan Pithadia. Columbus High School, Columbus, GA USA
  120. Charlotte Wells. Gloucester High School, Ottawa, Canada
  121. Silvi Qemo. Hon W.c Kennedy C.i., Windsor, Canada
  122. Aziz Alawadhi. Charles P. Allen, Halfiax, Canada
  123. Tori Kennedy. Brookstone School, Columbus, GA USA
  124. Amy Tanner. Evergreen Elemntary, Metamora, OH USA
  125. Mr Siebert. View Ridge Elementary, Everett, WA USA
  126. Sam Sunder. Worthington Park, Columbus, OH USA
  127. Tony Song. East Brunswick High School, East Brunswick, NJ USA
  128. Ryan Foster. Southern Polytechnic State University, Acworth, GA USA
  129. Gary Lemay. Cortex Medical, Atlanta, GA USA
  130. Travis Xiang. South Seminole Middle School, Casselberry, FL USA
  131. Jeremy Shoup. Mathnasium, Fort Collins, CO USA
  132. Michael Hagarty Quaroni. Gloucester High School, Ottawa, Canada
  133. Hal Keene. St. Cloud High School, Orlando, FL USA
  134. Ritwik Gupta. Pleasant Hills Middle School, Pittsburgh, PA USA
  135. Lim Li. Queenstown Primary School, Singapore, Singapore
  136. Lim Jeck. Nus High School Of Math & Science, Singapore, Singapore
  137. John Li Jieyang. Nan Hua High School, Singapore, Singapore
  138. Kerri Sweeney. Chelmsford High, Chelmsford, MA USA
  139. Edgar A. Cherry Hill West, Cherry Hill, NJ USA
  140. Mara Rubin. Wln, White Lake, MI USA
  141. Nick Buglak. Walled Lake Northern, Commerce Twp, MI USA
  142. Iris Rukshin. High Tech High School, Holmdel, NJ USA
  143. Jonathan He. Dickerson Middle School, Marietta, GA USA
  144. Nikhil Patel. Columbus High School, Columbus, GA USA
  145. Albert Tang. Lawrence Middle School, West Hills, CA USA
  146. Kevin Lee. Cherry Hill West High School, Cherry Hill, NJ USA
  147. Bar Greengrass. Hasachar School, Hod Hasaron, Israel
  148. Sandy Lee. Southridge School, Surrey, Canada
  149. Amr Khafagy. Dhahran School, Dhahran, Saudi Arabia
  150. Thirumalai Thathachary. Business, Sunnyvale, CA USA
  151. Ashwath Thirumalai. West Valley School, Sunnyvale, CA USA
  152. Osman Molumo. Dhahran Middle School, Dhahran, Saudi Arabia
  153. Steven Ferry. None, Gold Coast, Australia
  154. Monica Oprina. Economist, Piatra Neamt, Romania
  155. S Wolf. Ridgefield Academy, Ridgefield, CT USA
  156. Megan Ferry. Lake Norman Charter School, Denver, NC USA
  157. Jeffrey Schwartz. Boiling Springs High School, Boiling Springs, PA USA
  158. Ed Wern. <none>, Monticello, MN USA
  159. Paul Wei. Hon. Kennedy Collegiate Institute, Windsor, Canada
  160. Dominick Grosso. Glendale High School District, Phoenix, AZ USA
  161. Tri Dinh. Cherry Hill West, Cherry Hill, NJ USA
  162. Alex V.. Roosevelt Ms, Blaine, MN USA
  163. Houston Joel. Retired, Avon Lake, OH USA
  164. Alva Welch. Lenoir Community College, Snow Hill, NC USA
  165. Evelyn Chua. Southridge, Surrey, Canada
  166. Cristal Flanders. Behs, Bristol, CT USA
  167. Ning Ye. Charles.p.allen High School, Halifax, Nova Scotia, Canada
  168. Mathew Chethimattam. Business, Columbus, GA USA
  169. Gent Gjika. Turgut Ozal College Of Tirana, Tirana, Albania
  170. Katie Bishop. Southridge School, Surrey, Canada
  171. Andrew Abbott. Walled Lake Northern, Commerce, MI USA
  172. Tori Brggs. Shaw High, Midland, GA USA
  173. Albert Chung. Southridge School, White Rock, Canada
  174. Kamelia Aryafar. Drexel, Philadelphia, PA USA
  175. Nicolas Hite. Walled Lake Northern, West Bloomfield, MI USA
  176. Pana Gheorghe. 307 Ps Bucharest, Bucharest, Romania
  177. Jeffrey Ng. Cherry Hill West High School, Cherry Hill, NJ USA
  178. Steven Wu. St. Luke, Columbus, GA USA
  179. Sanjay Godse. Iit Bombay, Pune, India
  180. Alex Champe. Walled Lake Northern High School, Walled Lake, MI USA
  181. Khoa Pham. Lycée Claudel, Ottawa, Canada
  182. Jill Van Der Schaaf. Union Elementary, Union, ME USA
  183. Wendy Cheng. Cherry Hill West, Cherry Hill, NJ USA
  184. Carly Burton. Walled Lake Northern, Commerce, MI USA
  185. Keith Ray. Glenwood, Ellerslie, GA USA
  186. Lelouch Lamperouge. Cherry Hill West, Cherry Hill, NJ USA
  187. Way Tan. Nus High School, Singapore, Singapore
  188. Pasquale Petrosino. @tanks, Ivrea, Italy
  189. Joe Smith. Terry Parker High School, Jacksonville, FL USA
  190. Shaz R.. Gloucester High School, Ottawa, Canada
  191. Andrew Golczynski. Parkville High School, Baltimore, MD USA
  192. Brianna Blair. Hawbridge, Burlington, NC USA
  193. Howard Lam. N/a, San Diego, CA USA
  194. Bridget Hicks. Cherry Hill High School West, Cherry Hill, NJ USA
  195. Brittany Hale. Chelmsford High School, Chelmsford, MA USA
  196. Johnny Kang. Cherry Hill West, Cherry Hill, NJ USA
  197. Joshua Ani. Montgomery Elementary School, Atlanta, GA USA
  198. Tulasi Chittivelu. Peoria Academy, Peoria, IL USA
  199. Duc Ngo Minh. National University Of Singapore, Singapore, Singapore
  200. Daniel Wallberg. Loos Skola, Los, Sweden
  201. Alec Sun. Florence Sawyer School, Bolton, MA USA
  202. Regan Parmentier. Walled Lake Northerm, Commerce, MI USA
  203. Casey Nosiglia. South Salem High School, Salem, OR USA
  204. Jean-Guy Smith. none, Sorel-tracy, Qc, Canada
  205. Matt Drawz. UHC, Saint Paul, MN USA
  206. Kirk Ticknor. Blackmon Road Middle, Columbus, GA USA
  207. Sérgio Duarte Da Silva. Univ. Coimbra, Viana Do Castelo, Portugal
  208. Kate Wettergreen. , Pittsburgh, PA USA
  209. Paige Espinosa. Cherry Hill West, Cherry Hill, NJ USA
  210. Tierra Jones. Shaw High School, Columbus, GA USA
  211. Mitchell Renteria. High School West, Cherry Hill, NJ USA
  212. Andrew Adorno. Chhs West, Cherry Hill, NJ USA
  213. Ebone Monk. Columbus High, Columbus, GA USA
  214. Mike Hilst. , Spring Lake Park, MN USA
  215. Sophie Lee. Peoria Academy, Peoria, IL USA
  216. Deeti Pithadia. Columbus High School, Columbus, GA USA
  217. John Kim. Gloucester High School, Ottawa, Canada
  218. Grant Harriss. Osceola Middle School, Ocala, FL USA
  219. Largesa Loga. Hon. W. C. Kennedy Collegiate Institute, Windsor, Canada
  220. Adam Cohen. Brwon, Providence, RI USA
  221. Jamie Searles. Newport Harbor High School, Newport Beach, CA USA
  222. William Heuton. Hon. Kennedy Ci, Windsor, Canada
  223. Quinn Harrington. Hon Kennedy Ci, Windsor, Canada
  224. Eric Hays. Cherry Hill High School West, Cherry Hill, NJ USA
  225. Alexa Piacenza. Chs, Chelmsford, MA USA
  226. Alyssa Sims. Cherry Hill West, Cherry Hill, NJ USA
  227. Seungkwon Lee. Blackmon Rd Middle School, Columbus, GA USA
  228. Sahar Dawi. Kennedy Collegiate Institute, Windsor, Canada
  229. Dave Lichtenberger. Cherry Hillz West, Cherry Hillllllllllllllllllllllllllllllllllllllll, NJ USA
  230. Jarvi Kim. Southridge School, Surrey, Canada
  231. Ashley Radee. Peoria Academy, Peoria, IL USA
  232. Elain Smith. D, Dornoch, Scotland
  233. Robin Molin. Los Skola, Los, Sweden
  234. Masanori Shimizu. Kamedanishi　JHS, Niigata, Japan
  235. Abdullah Al Smoudi. Hon. W.c. Kennedy Ci, Windsor, Canada
  236. Spencer Nuff. Honourable W.c. Kennedy Collegiate Institute, Windsor, Canada
  237. Seph Marshall. St. Raymond, Toronto, Canada
  238. Zina Hlobil. Brillantmont International School, Lausanne, Switzerland
  239. Nirenjen Sunil. Chempaka, Trivandrum, India
  240. Yun He. Mayde Creek, Houston, TX USA
  241. Christopher Foster. Utah Valley University, Orem, UT USA
  242. Xianli Fu. Khartoum American School, Puyang, Henan, China
  243. Fouad Nader. Hon. W.c. Kennedy Collegiate Institute, Windsor, Canada
  244. Mary-ann Ionascu. Columbus High School, Columbus, GA USA
  245. Christine Nguyen. Cherry Hill High School West, Cherry Hill, NJ USA
  246. Kian Oconnor. Crane, Santa Barbara, CA USA
  247. Imman Jami. Gloucester High School, Ottawa, Canada
  248. Elizabeth Kim. Southridge, Surrey, Canada
  249. Chris Kim. Southridge, Surrey, Canada
  250. Tiffany Winchester. Columbus High School, Columbus, GA USA
  251. Alissa Dillon. Columbus High School, Columbus, GA USA
  252. Dwayne Spruell. Shaw High School, Columbus, GA USA
  253. Timoty Ng. Southridge School, Surrey, Bc, Canada
  254. Brady Wern. Monticello High School, Monticello, MN USA
  255. Chris Chesnik. Hon. W.c. Kennedy Collegiate Institute, Windsor, Canada
  256. Nii-ofei Dodoo. Cherry Hill High School West, Cherry Hill, NJ USA
  257. Kaitlyn Kinney. Walled Lake Northern High School, Commerce, MI USA
  258. Ai Nguyen Year 7m. Abc International Shool, Ho Chi Minh City, Vietnam
  259. Jenna D. Mesa Union School, Camarillo, CA USA
  260. Marna Dunne. West, Cherry Hill, NJ USA
  261. Emily Takagi. Columbus High School, Columbus, GA USA
  262. Victor Chong. Columbus High School, Columbus, GA USA
  263. Nick Schilling. Walled Lake Northern, White Lake, MI USA
  264. Denisa Dupu. Creekwood Middle School, Houston, TX USA
  265. Kirk Lam. Hong Kong International School, Hong Kong, Hong Kong
  266. Sydney Weaver. Brookstone High School, Columbus, GA USA
  267. Aijalon Cobb. Shaw High School, Columbus, GA USA
  268. Christian Sanchez. Uiuc, Chamapaign, IL USA
  269. Zeinab Ammar. Kennedy.c.i, Windsor, Canada
  270. Zoe B. Cherry Hill West Highschool, Cherry Hill, NJ USA
  271. Frank Sysko. Nazareth High School, Nazareth, PA USA
  272. Meredith Ray. Cms, Kingwood, TX USA
  273. Carlos Gomez. Uga, Athens, GA USA
  274. Kenneth Jobe Krebs. Walled Lake Northern, White Lake, MI USA
  275. Jim Stein. Bunnell H.S., Stratford, CT USA
  276. Erik Topness. Sales, Preston, MN USA
  277. Montavious Thomas. Randolph-clay High School, Lumpkin, GA USA
  278. Joseph Abrams. Mtu, Houghton, MI USA
  279. Olivia Bodman. Washington Township High School, Sewell, NJ USA
  280. John Dall. , Greenlawn, NY USA
  281. Lauren Zachman. Msa, Woodbury, MN USA
  282. Emily Martines. Cherry Hill High School West, Cherry Hill, NJ USA
  283. Gianna Flamini. Cherry Hill Highschool West, Cherry Hill, NJ USA
  284. Mike Ditullio. Washington Township High School, Sicklerville, NJ USA
  285. Jillian Lee. Landmark Christian School, Sandy Springs, GA USA
  286. Srirashmi Gudur. Britt David Magnet School, Columbus, GA USA
  287. Jim Tobakos. Walled Lake Northern High School, White Lake, MI USA
  288. Nicholas Antonov. The Rugby School At Woodfield, Neptune, NJ USA
  289. Mira Liu. International School Of Beijing, Beijing, China
  290. Alan Upton. Columbusstateuniversity, Columbus, GA USA
  291. Nick Majie. Walled Lake Northern High School, Commerce Township, MI USA
  292. Ari Van Der Merwe. Home School, Jerusalem, Israel
  293. Shannon Greenbaum. Boiling Springs High School, Carlisle, PA USA
  294. Judy Pennington-Price. Eastern Kentucky University, Annville, KY USA
  295. Mohamed Ahmed. Gloucester High School, Ottawa, Canada
  296. Ali Hassan. Gloucester High School, Ottawa, Canada
  297. Tanner Sandlin. Jackson County High School, Mckee, KY USA
  298. Jeremy Rotblat. Cherry Hill High School West, Cherry Hill, NJ USA
  299. Jenny Duong. Hon. W. C. Kennedy Collegiate Institute, Windsor, Canada
  300. Chiriac Corina. "gr. C. Moisil" High School, Buzau, Romania
  301. Joanna Birns. Mesa Union School, Somis, CA USA
  302. Robert Segrest. Cherry Hill Hich School West, Cherry Hill, NJ USA
  303. Megan Michaels. Washington Township High School, Sewell, NJ USA
  304. Hussein Assaf. Gloucester Hs, Ottawa, Canada
  305. Mary Lou Jarrell. Brookstone School, Columbus, GA USA
  306. Brooke Napier. Glenwood School, Phenix City, AL USA
  307. Jeff Lam. Hong Kong International School, Hong Kong, Hong Kong
  308. Phillip Patterson. Landmark Christian School, Fairburn, GA USA
  309. Ariel Tynan. Sonoran Sky, Phoenix, AZ USA
  310. Serena Chow. Mesa Union School, Oxnard, CA USA
  311. Andy Livernois. Walled Lake Northern, Commerce, MI USA