Santa Clara University High School Mathematics Contest

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.) Student must not make use of cell-phones or MP3 players (or similar devices) during the exam.

The 2006 Contest will be held on Saturday, November 11, 2006.

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.

As examples of the type of questions asked, the fifth problem on the 2005 exam was:

How many distinct (that is, noncongruent) trangles are there with all sides of integer length, with the longest side (or sides) having length 2005?

If a and b are numbers such that a - b = 4 and a² - b² = 44, what integer is a³ - b³?

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).

Find a positive integer a that satisfies the equation a^a - (a - 1)^a+1 = 13.

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?

Find the largest positive integer e for which 3^e is an exact divisor of 1998.

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 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.

Last Updated: 27 September 2006
Maintainer: webmaster@math.scu.edu