Sydney University Mathematics Society

SUMS Problem Competition

This competition is open to undergraduates (including Honours students) at any Australian university or tertiary institution. Entrants may use any souce of information except other people.

Entrants may submit solutions to as many problems as they wish. Prizes ($60 book vouchers from the Co-op Bookshop) will be awarded for the best correct solution to each of the 10 problems. Students from the University of Sydney are also eligible for the Norbert Quirk Prizes, based on the overall quality of their entry (one for each of 1st, 2nd and 3rd years). Extensions and generalizations of any problem are invited and are taken into account when assessing solutions. If two or more solutions to a problem are essentially equal, preference may be given to students in the earlier year of university; otherwise, prizes may be shared. If a problem receives no correct solutions, its prize-money will be redistributed among the other problems.

Entries must be received by Friday, September 5, 2008. They may be posted to Dr Anthony Henderson, School of Mathematics and Statistics, The University of Sydney, NSW 2006, or delivered in person to Room 805, Carslaw Building. Please mark your entry SUMS Problem Competition 2008, and include your name, university, student number, year of study, and postal address for the return of your entry and prizes.

2008 Competition

Here are the 2008 problems.

Clarification of Q9: the five distinct unit vectors should not just be distinct; no two should be (complex) scalar multiples of each other.

Past Competitions

Here are the recent SUMS Competition problems and solutions: