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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Congratulations to Phillip Patterson of Fairburn, GA, this week's winner of the Problem of the Week T-shirt! Find out more about winning a prize.

40% of the submitted answers were correct. (351 out of 880)
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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. STEVEN EASTOP. NORTHDOWN COUNTY PRIMARY SCHOOL, MARGATE, KENT. UK, MARGATE, KENT, UK, United Kingdom
  28. Rahul Sushil. School, Dhahran, Saudi Arabia
  29. Nabiel Hilmy Abuyazid. Dhahran School, Dhahran, Saudi Arabia
  30. Jaime Liew. Mercedes College, Adelaide, Australia
  31. Frans Janssen. Nijmegen, Netherlands
  32. Andrew Xu. Lowell High School, San Francisco, CA USA
  33. Rishi Kant Brahmpuria. Maulana Azad National Institute Of Technology, Bhopal, India
  34. Peter Lindgren. Slotte, Ljusdal, Sweden
  35. Young Joo Park. Student, Seoul, Korea (south)
  36. Anneleen Van Geenhoven. Ua, Antwerp, Belgium
  37. Dani Chavez. Creekwood Middle School!, Kingwood, TX USA
  38. Alan Drayton. International School Manila, Manila, Philippines
  39. Stephen Bidwell. Bridge Creek Elementary, Elgin, SC USA
  40. Ed Wilson. Eku, Richmond, KY USA
  41. Graham Gilbert. Retired Teacher, Haddon Hts, NJ USA
  42. Rakesh M. Business, New Delhi, India
  43. Kendrick Wong. Nus High School, Singapore, Singapore
  44. Mike Schieffer. None, Austin, TX USA
  45. Evamgelos Kyriakidis. Ntua, Athens, Greece
  46. Thomas Newsome. Weaver Academy, Greensboro, NC USA
  47. E. Rives. Uahuntsville, Huntsville, AL USA
  48. Janet Yang. N/a, Ridgewood, NJ USA
  49. Joe Neumann. Washington Township High School, Sewell, NJ USA
  50. Michael Strezebonski. Lincoln Trail, Mahomet, IL USA
  51. Chuanqi Shen. Raffles Institution, Singapore, Singapore
  52. Cody Woosoncroft. Northeast High School, Pasadena, MD USA
  53. Jim Hart. Coastal Carolina Community College, Jacksonville, NC USA
  54. Filip Goldefus. Brno University Of Technology, Brno, Czech Republic
  55. Yung-kuang Wang. Guangfu Junior High School, Taipei, Taiwan
  56. Gary Brensike. Saic, Germantown, MD USA
  57. Fengyuan Zhou. Hon.w.c.kennedy.c.i, Windsor, Canada
  58. Richard Ethier. Hon.w.c. Kenndy Ci., Windsor, Canada
  59. Maura Mackenzie. Berkshire, Sheffield, MA USA
  60. Edward Freeman. Uconn, West Hartford, CT USA
  61. Jon Scheck. N/A, New York, NY USA
  62. Shikhar Maheshwari. Bi, Mumbai, Mumbai, India
  63. Michael Coon. Niobrara County High School, Lusk, WY USA
  64. Sam Wright. Chelmsford High School, Chelmsford, MA USA
  65. Basil Kilisav. Qvi, Rochester, NY USA
  66. Bob Mitchell. None, Normal, IL USA
  67. Jelios Roytman. Ps 158, New York, NY USA
  68. Emily Dougelus. Bryan High, Bryan, TX USA
  69. Eugene Roytman. ., New York, NY USA
  70. Dan Brandt. Rga, St. Louis, MO USA
  71. Jonathan Foster. N/A, Sacramento, CA USA
  72. Gerald Queenan. Retired, Pawtucket, RI USA
  73. Graham Adams. Homeschool, Hoschton, GA USA
  74. Daniel (bobby) Newkirk. Lakeside Highschool, Martinez, GA USA
  75. Alan Best. Midtown, New York, NY USA
  76. Bobby Jordan. Lakeside High School, Martinez, GA USA
  77. Connie Chen. Amador Valley High School, Pleasanton, CA USA
  78. Cheryl Hampel. St. Marys Magnet Academy, Columbus, GA USA
  79. Mark Enderich. Wayne State University, Plymouth, MI USA
  80. Pat Costello. Eku, Richmond, KY USA
  81. Sergio Leonardi. None, Houston, TX USA
  82. Gordon Bockus. Wilburton High School, Wilburton, OK USA
  83. Alan Moroz. Hon. W.c. Kennedy C.i., Windsor, On, Canada
  84. Zack Manasco. Niobrara County High School, Lusk, WY USA
  85. Bobby Markey. E.c. Glass High School, Lynchburg, VA USA
  86. Tent Eddies. Self-employed, Casselberry, FL USA
  87. John Macauda. Madison Middle, Trumbull, CT USA
  88. Brad Woods. N/A, Stonewall, Canada
  89. Meera Gopal. Business, Bridgewater, NJ USA
  90. Meera Kumar. Business, Bridgewater, NJ USA
  91. Meera Kumar. Business, Bridgewater, NJ USA
  92. Kristopher Skotek. Columbus School, Carteret, NJ USA
  93. Daniel Lopez Aguayo. Mathematics, Puebla, Mexico
  94. Armand Bajrami. Kennedy Collegiate Institute Highschool, Windsor, Canada
  95. Henri Zheku. Hon. W.c. Kennedy Collegiate Institute, Windsor, Canada
  96. David Zeng. Stuyvesant, Brooklyn, NY USA
  97. Kalpana Vijayakumar. Business, Bridgewater, NJ USA
  98. Jake Spivey. Niobrara County High School, Lusk, WY USA
  99. L. Zhou. Middle, Parsippany, NJ USA
  100. Hoa Tang. C.p.allen, Bedford, Canada
  101. Richard Wile. Charles P. Allen High School, Bedford, Nova Scotia, Canada
  102. Feng Shi. Shen Pan Zhe, Shenzhen, China
  103. Joe Cochran. Landmark Christian School, Fayetteville, GA USA
  104. Douglas Hauser. Biomedical Research At Usc, Los Angeles, CA USA
  105. Shaun Lising. Cherry Hill West High School, Cherry Hill, USA
  106. Qc Marniche. Cherry Hill West, Cherry Hill, NJ USA
  107. Robert Karch. N/a, Greenwich, CT USA
  108. Neha Kumar. Sms, Memphis, TN USA
  109. Tomas Farmer. Southridge School, Vancouver, DC Canada
  110. Bemjamin Hsu. Gloucester High School, Ottawa, Canada
  111. Max Li. Gloucester High School, Ottawa, Canada
  112. Paula A.. Gloucester High School, Ottawa, Canada
  113. Lily Loo. Kennesaw, Columbus, GA USA
  114. Vernick Bashi. Walled Lake Northern High School, Commerce Township, MI USA
  115. Rosa Paulina Anajao. University Of Santo Tomas, Quezon City, Philippines
  116. Angel Stoychev. Aprilov National High School, Gabrovo, Bulgaria
  117. Rui Guo. Na, Lawrence, KS USA
  118. Martina Bray. Eastern Kentucky University, Manchester, KY USA
  119. Akhil Enjety. Hon.w.ckennedy C.i, Windsor, Canada
  120. Kishan Pithadia. Columbus High School, Columbus, GA USA
  121. Charlotte Wells. Gloucester High School, Ottawa, Canada
  122. Silvi Qemo. Hon W.c Kennedy C.i., Windsor, Canada
  123. Aziz Alawadhi. Charles P. Allen, Halfiax, Canada
  124. Tori Kennedy. Brookstone School, Columbus, GA USA
  125. Amy Tanner. Evergreen Elemntary, Metamora, OH USA
  126. Mr Siebert. View Ridge Elementary, Everett, WA USA
  127. Sam Sunder. Worthington Park, Columbus, OH USA
  128. Tony Song. East Brunswick High School, East Brunswick, NJ USA
  129. Ryan Foster. Southern Polytechnic State University, Acworth, GA USA
  130. Gary Lemay. Cortex Medical, Atlanta, GA USA
  131. Travis Xiang. Hogwarts School of Witchcraft and Wizardry, Casselberry, FL USA
  132. Jeremy Shoup. Mathnasium, Fort Collins, CO USA
  133. Michael Hagarty Quaroni. Gloucester High School, Ottawa, Canada
  134. Hal Keene. St. Cloud High School, Orlando, FL USA
  135. Ritwik Gupta. Pleasant Hills Middle School, Pittsburgh, PA USA
  136. Lim Li. Queenstown Primary School, Singapore, Singapore
  137. Lim Jeck. Nus High School Of Math & Science, Singapore, Singapore
  138. John Li Jieyang. Nan Hua High School, Singapore, Singapore
  139. Kerri Sweeney. Chelmsford High, Chelmsford, MA USA
  140. Edgar A. Cherry Hill West, Cherry Hill, NJ USA
  141. Mara Rubin. Wln, White Lake, MI USA
  142. Nick Buglak. Walled Lake Northern, Commerce Twp, MI USA
  143. Iris Rukshin. High Tech High School, Holmdel, NJ USA
  144. Jonathan He. Dickerson Middle School, Marietta, GA USA
  145. Nikhil Patel. Columbus High School, Columbus, GA USA
  146. Albert Tang. Lawrence Middle School, West Hills, CA USA
  147. Kevin Lee. Cherry Hill West High School, Cherry Hill, NJ USA
  148. Bar Greengrass. Hasachar School, Hod Hasaron, Israel
  149. Sandy Lee. Southridge School, Surrey, Canada
  150. Amr Khafagy. Dhahran School, Dhahran, Saudi Arabia
  151. Thirumalai Thathachary. Business, Sunnyvale, CA USA
  152. Ashwath Thirumalai. West Valley School, Sunnyvale, CA USA
  153. Osman Molumo. Dhahran Middle School, Dhahran, Saudi Arabia
  154. Steven Ferry. None, Gold Coast, Australia
  155. Monica Oprina. Economist, Piatra Neamt, Romania
  156. Dinesh Nayak. Canara High School, Mangalore, India
  157. S Wolf. Ridgefield Academy, Ridgefield, CT USA
  158. Megan Ferry. Lake Norman Charter School, Denver, NC USA
  159. Jeffrey Schwartz. Boiling Springs High School, Boiling Springs, PA USA
  160. Ed Wern. <none>, Monticello, MN USA
  161. Paul Wei. Hon. Kennedy Collegiate Institute, Windsor, Canada
  162. Dominick Grosso. Glendale High School District, Phoenix, AZ USA
  163. Tri Dinh. Cherry Hill West, Cherry Hill, NJ USA
  164. Alex V.. Roosevelt Ms, Blaine, MN USA
  165. Houston Joel. Retired, Avon Lake, OH USA
  166. Alva Welch. Lenoir Community College, Snow Hill, NC USA
  167. Evelyn Chua. Southridge, Surrey, Canada
  168. Cristal Flanders. Behs, Bristol, CT USA
  169. Ning Ye. Charles.p.allen High School, Halifax, Nova Scotia, Canada
  170. Mathew Chethimattam. Business, Columbus, GA USA
  171. Gent Gjika. Turgut Ozal College Of Tirana, Tirana, Albania
  172. Katie Bishop. Southridge School, Surrey, Canada
  173. Andrew Abbott. Walled Lake Northern, Commerce, MI USA
  174. Tori Brggs. Shaw High, Midland, GA USA
  175. Albert Chung. Southridge School, White Rock, Canada
  176. Kamelia Aryafar. Drexel, Philadelphia, PA USA
  177. Nicolas Hite. Walled Lake Northern, West Bloomfield, MI USA
  178. Pana Gheorghe. 307 Ps Bucharest, Bucharest, Romania
  179. Jeffrey Ng. Cherry Hill West High School, Cherry Hill, NJ USA
  180. Steven Wu. St. Luke, Columbus, GA USA
  181. Sanjay Godse. Iit Bombay, Pune, India
  182. Alex Champe. Walled Lake Northern High School, Walled Lake, MI USA
  183. Khoa Pham. Lycée Claudel, Ottawa, Canada
  184. Jill Van Der Schaaf. Union Elementary, Union, ME USA
  185. Wendy Cheng. Cherry Hill West, Cherry Hill, NJ USA
  186. Carly Burton. Walled Lake Northern, Commerce, MI USA
  187. Keith Ray. Glenwood, Ellerslie, GA USA
  188. Lelouch Lamperouge. Cherry Hill West, Cherry Hill, NJ USA
  189. Way Tan. Nus High School, Singapore, Singapore
  190. Pasquale Petrosino. @tanks, Ivrea, Italy
  191. Joe Smith. Terry Parker High School, Jacksonville, FL USA
  192. Shaz R.. Gloucester High School, Ottawa, Canada
  193. Andrew Golczynski. Parkville High School, Baltimore, MD USA
  194. Brianna Blair. Hawbridge, Burlington, NC USA
  195. Howard Lam. N/a, San Diego, CA USA
  196. Bridget Hicks. Cherry Hill High School West, Cherry Hill, NJ USA
  197. Brittany Hale. Chelmsford High School, Chelmsford, MA USA
  198. Johnny Kang. Cherry Hill West, Cherry Hill, NJ USA
  199. Joshua Ani. Montgomery Elementary School, Atlanta, GA USA
  200. Tulasi Chittivelu. Peoria Academy, Peoria, IL USA
  201. Duc Ngo Minh. National University Of Singapore, Singapore, Singapore
  202. Daniel Wallberg. Loos Skola, Los, Sweden
  203. Alec Sun. Florence Sawyer School, Bolton, MA USA
  204. Regan Parmentier. Walled Lake Northerm, Commerce, MI USA
  205. Casey Nosiglia. South Salem High School, Salem, OR USA
  206. Jean-Guy Smith. none, Sorel-tracy, Qc, Canada
  207. Matt Drawz. UHC, Saint Paul, MN USA
  208. Kirk Ticknor. Blackmon Road Middle, Columbus, GA USA
  209. Sérgio Duarte Da Silva. Univ. Coimbra, Viana Do Castelo, Portugal
  210. Kate Wettergreen. , Pittsburgh, PA USA
  211. Paige Espinosa. Cherry Hill West, Cherry Hill, NJ USA
  212. Tierra Jones. Shaw High School, Columbus, GA USA
  213. Mitchell Renteria. High School West, Cherry Hill, NJ USA
  214. Andrew Adorno. Chhs West, Cherry Hill, NJ USA
  215. Ebone Monk. Columbus High, Columbus, GA USA
  216. Mike Hilst. , Spring Lake Park, MN USA
  217. Sophie Lee. Peoria Academy, Peoria, IL USA
  218. Deeti Pithadia. Columbus High School, Columbus, GA USA
  219. John Kim. Gloucester High School, Ottawa, Canada
  220. Grant Harriss. Osceola Middle School, Ocala, FL USA
  221. Largesa Loga. Hon. W. C. Kennedy Collegiate Institute, Windsor, Canada
  222. Adam Cohen. Brwon, Providence, RI USA
  223. Jamie Searles. Newport Harbor High School, Newport Beach, CA USA
  224. William Heuton. Hon. Kennedy Ci, Windsor, Canada
  225. Quinn Harrington. Hon Kennedy Ci, Windsor, Canada
  226. Eric Hays. Cherry Hill High School West, Cherry Hill, NJ USA
  227. Alexa Piacenza. Chs, Chelmsford, MA USA
  228. Alyssa Sims. Cherry Hill West, Cherry Hill, NJ USA
  229. Seungkwon Lee. Blackmon Rd Middle School, Columbus, GA USA
  230. Sahar Dawi. Kennedy Collegiate Institute, Windsor, Canada
  231. Dave Lichtenberger. Cherry Hillz West, Cherry Hillllllllllllllllllllllllllllllllllllllll, NJ USA
  232. Jarvi Kim. Southridge School, Surrey, Canada
  233. Ashley Radee. Peoria Academy, Peoria, IL USA
  234. Elain Smith. D, Dornoch, Scotland
  235. Robin Molin. Los Skola, Los, Sweden
  236. Masanori Shimizu. Kamedanishi?JHS, Niigata, Japan
  237. Abdullah Al Smoudi. Hon. W.c. Kennedy Ci, Windsor, Canada
  238. Spencer Nuff. Honourable W.c. Kennedy Collegiate Institute, Windsor, Canada
  239. Christine Zeltway. St. Raymond Gifted Centre, Toronto, Canada
  240. Zina Hlobil. Brillantmont International School, Lausanne, Switzerland
  241. Nirenjen Sunil. Chempaka, Trivandrum, India
  242. Yun He. Mayde Creek, Houston, TX USA
  243. Christopher Foster. Utah Valley University, Orem, UT USA
  244. Xianli Fu. Khartoum American School, Puyang, Henan, China
  245. Fouad Nader. Hon. W.c. Kennedy Collegiate Institute, Windsor, Canada
  246. Mary-ann Ionascu. Columbus High School, Columbus, GA USA
  247. Christine Nguyen. Cherry Hill High School West, Cherry Hill, NJ USA
  248. Kian Oconnor. Crane, Santa Barbara, CA USA
  249. Imman Jami. Gloucester High School, Ottawa, Canada
  250. Elizabeth Kim. Southridge, Surrey, Canada
  251. Chris Kim. Southridge, Surrey, Canada
  252. Tiffany Winchester. Columbus High School, Columbus, GA USA
  253. Alissa Dillon. Columbus High School, Columbus, GA USA
  254. Dwayne Spruell. Shaw High School, Columbus, GA USA
  255. Timoty Ng. Southridge School, Surrey, Bc, Canada
  256. Brady Wern. Monticello High School, Monticello, MN USA
  257. Chris Chesnik. Hon. W.c. Kennedy Collegiate Institute, Windsor, Canada
  258. Nii-ofei Dodoo. Cherry Hill High School West, Cherry Hill, NJ USA
  259. Kaitlyn Kinney. Walled Lake Northern High School, Commerce, MI USA
  260. Ai Nguyen Year 7m. Abc International Shool, Ho Chi Minh City, Vietnam
  261. Jenna D. Mesa Union School, Camarillo, CA USA
  262. Marna Dunne. West, Cherry Hill, NJ USA
  263. Emily Takagi. Columbus High School, Columbus, GA USA
  264. Victor Chong. Columbus High School, Columbus, GA USA
  265. Nick Schilling. Walled Lake Northern, White Lake, MI USA
  266. Denisa Dupu. Creekwood Middle School, Houston, TX USA
  267. Kirk Lam. Hong Kong International School, Hong Kong, Hong Kong
  268. Sydney Weaver. Brookstone High School, Columbus, GA USA
  269. Aijalon Cobb. Shaw High School, Columbus, GA USA
  270. Christian Sanchez. Uiuc, Chamapaign, IL USA
  271. Zeinab Ammar. Kennedy.c.i, Windsor, Canada
  272. Zoe B. Cherry Hill West Highschool, Cherry Hill, NJ USA
  273. Marty Portle. Nazareth High School, Nazareth, PA USA
  274. Meredith Ray. Cms, Kingwood, TX USA
  275. Carlos Gomez. Uga, Athens, GA USA
  276. Kenneth Jobe Krebs. Walled Lake Northern, White Lake, MI USA
  277. Jim Stein. Bunnell H.S., Stratford, CT USA
  278. Erik Topness. Sales, Preston, MN USA
  279. Montavious Thomas. Randolph-clay High School, Lumpkin, GA USA
  280. Joseph Abrams. Mtu, Houghton, MI USA
  281. Olivia Bodman. Washington Township High School, Sewell, NJ USA
  282. John Dall. , Greenlawn, NY USA
  283. Lauren Zachman. Msa, Woodbury, MN USA
  284. Emily Martines. Cherry Hill High School West, Cherry Hill, NJ USA
  285. Gianna Flamini. Cherry Hill Highschool West, Cherry Hill, NJ USA
  286. Mike Ditullio. Washington Township High School, Sicklerville, NJ USA
  287. Jillian Lee. Landmark Christian School, Sandy Springs, GA USA
  288. Srirashmi Gudur. Britt David Magnet School, Columbus, GA USA
  289. Jim Tobakos. Walled Lake Northern High School, White Lake, MI USA
  290. Nicholas Antonov. The Rugby School At Woodfield, Neptune, NJ USA
  291. Mira Liu. International School Of Beijing, Beijing, China
  292. Alan Upton. Columbusstateuniversity, Columbus, GA USA
  293. Nick Majie. Walled Lake Northern High School, Commerce Township, MI USA
  294. Ari Van Der Merwe. Home School, Jerusalem, Israel
  295. Shannon Greenbaum. Boiling Springs High School, Carlisle, PA USA
  296. Judy Pennington-Price. Eastern Kentucky University, Annville, KY USA
  297. Mohamed Ahmed. Gloucester High School, Ottawa, Canada
  298. Ali Hassan. Gloucester High School, Ottawa, Canada
  299. Tanner Sandlin. Jackson County High School, Mckee, KY USA
  300. Jeremy Rotblat. Cherry Hill High School West, Cherry Hill, NJ USA
  301. Jenny Duong. Hon. W. C. Kennedy Collegiate Institute, Windsor, Canada
  302. Chiriac Corina. "gr. C. Moisil" High School, Buzau, Romania
  303. Joanna Birns. Mesa Union School, Somis, CA USA
  304. Robert Segrest. Cherry Hill Hich School West, Cherry Hill, NJ USA
  305. Megan Michaels. Washington Township High School, Sewell, NJ USA
  306. Hussein Assaf. Gloucester Hs, Ottawa, Canada
  307. Mary Lou Jarrell. Brookstone School, Columbus, GA USA
  308. Brooke Napier. Glenwood School, Phenix City, AL USA
  309. Jeff Lam. Hong Kong International School, Hong Kong, Hong Kong
  310. Phillip Patterson. Landmark Christian School, Fairburn, GA USA
  311. Ariel Tynan. Sonoran Sky, Phoenix, AZ USA
  312. Serena Chow. Mesa Union School, Oxnard, CA USA
  313. Andy Livernois. Walled Lake Northern, Commerce, MI USA