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Santa Clara University
High School Mathematics Contest
50th Anniversary Year
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Since 1958, the Department of Mathematics and Computer Science
at Santa Clara University
has sponsored, as a community outreach, an annual High School
Mathematics Contest usually scheduled on the second Saturday
in November. This is a three hour exam which tests problem solving
skills and mathematical ingenuity rather than being directed toward the
content of a specific course.
Calculators and computers may NOT be used. (Students should also bring enough pre-sharpened pencils since no pencil sharpeners are available.) Students must not make use of cell-phones or MP3 players (or similar devices) during the exam.
The 2007 contest, the 50th such contest, was held
the morning of Saturday, November 10, 2007, from approximately 9am until noon.
Each year in October, letters are sent to high schools in the Bay Area inviting them to request tickets for those students interested in participating. Schools who have not received letters by November 1, should contact the Department at the number given below.
The following are examples of the type of questions asked:
- What is the largest number n < 2007 which can be written as the sum of five consecutive perfect squares? (2007 exam, prob 2)
- If x + y = 1 and x2 + y2 = 2, what is the value of (a) xy, (b) x3 + y3? (Write your answer without the use of operations [+, -, etc., ... or square roots].) (2006 exam, prob 3)
- How many distinct (that is, noncongruent) triangles are there with all sides of integer length, with the longest side (or sides) having length 2005? (2005 exam, prob 5)
- If a and b are numbers such that a - b = 4 and a2 - b2 = 44, what integer is a3 - b3? (2004 exam, prob 4)
- A positive integer n, when written in base b, has the form 211. When n is written in base b+2, it has the form 110. Determine n and b (in base 10). (2001 exam, prob 4)
- Find a positive integer a that satisfies the equation aa - (a - 1)a+1 = 13. (2000 exam, prob 1)
- In how many ways can the numbers 1, 2, 3, 4, 5, 6 be arranged as a sequence u, v, w, x, y, z such that u + x = v + y = w + z? (1999 exam, prob 3)
- Find the largest positive integer e for which 3e is an exact divisor of 1998. (1998 exam, prob 1)
The first twenty-five exams were published in the book, Santa Clara Silver Anniversary Contest Book, by G.L. Alexanderson, A. Hillman, L.F. Klosinski, D. Logothetti (Palo Alto: Dale Seymour Publications, 1985). (This book is now out of print.)
Statistics about recent exams are:
- November 10, 2007, 50th Contest, 277 contestants.
- November 11, 2006, 49th Contest, 255 contestants.
- November 12, 2005, 48th Contest, 275 contestants.
- November 13, 2004, 47th Contest, 258 contestants.
- November 8, 2003, 46th Contest, 230 contestants.
- November 9, 2002, 45th Contest, 238 contestants.
- November 10, 2001, 44th Contest, 143 contestants.
- November 11, 2000, 43rd Contest, 254 contestants.
- November 13, 1999, 42nd Contest, 232 contestants.
- November 14, 1998, 41st Contest, 363 contestants.
- November 15, 1997, 40th Contest, 384 contestants.
- November 16, 1996, 39th Contest, 358 contestants.
- November 11, 1995, 38th Contest, 296 contestants.
- November 12, 1994, 37th Contest, 298 contestants.
Information about the contest and forms requesting admission tickets are sent to schools in the San Francisco Bay Area in early October each year.
Further information can be obtained by contacting Prof. Leonard F. Klosinski at 408-554-6897 or Ms. Mary Asuncion at 408-554-4525 (to obtain a form for the admission tickets).
Maintainer: webmaster at math.scu.edu
Last Updated: 10 November 2007