Welcome to the website of the inaugural Contest in PRoblem-solving for Irish Second level Mathematicians (PRISM).

News and Announcements

The PRISM contest took place on October 19 in 200 Irish schools. Thank you to all the students and teachers who took part - we hope that you enjoyed the experience. The junior and senior PRISM problems for 2006 are now available. Answers are now available here.
Full solutions of the senior problems are available here.
Full solutions of the junior problems will follow shortly.

PRISM results will be posted by November 16.

PRISM 2006 is generously supported by

What is PRISM?

PRISM is a mathematical challenge for Irish second level students.
It will be held in participating schools on the afternoon of Thursday October 19 as part of Maths Week Ireland , and will include separate contests for pre-Junior Certificate and post-Junior Certificate students. Each will feature a series of twenty problems to challenge the problem-solving dexterity of participants. Each problem will be in multiple choice format with five options.

Why PRISM?

The specific aims of PRISM are as follows.

Who is it for?

Every second level student in Ireland is invited to participate in PRISM. If you enjoy puzzles or brainteasers, sudokus, logic problems, etc, this event is for you. If you like thinking about knotty mathematical problems, it is for you. If you enjoy mathematics at school, it is for you. If you just like to give your brain a workout, it is for you. If the sample problems posted here appeal to you, then it is definitely for you. Further sample problems (with answers) will be posted shortly.

Registration and Administration

Registration for PRISM closed on October 1st. We are delighted to report that 152 schools and nearly 6000 students have registered. The list of participating schools can be found here. If you are the contact person in a school and have not yet let us know the number of students expected, please do so no later than Thursday October 5. Contact details are as follows. Each participating school will receive a contest pack no later than October 16. This will contain the contest problems, answer sheets, PRISM ID numbers for the school's contestants, and some further information including instructions on filling out the answer sheets. Some of this material will need to be photocopied before the contest. Completed answer sheets should be returned to one of the PRISM organisers as advised in the pack, as soon as possible after the contest. Marking of answer sheets will be done by optical reader at NUI Galway, UCD and possibly other venues. Because the answer sheets will be (mostly) read by machine it is extremely important that they be filled out correctly. An incorrectly filled sheet from a single contestant may jeopardize not only that contestant's entry but the entire entry from his or her school.

Rules and Guidelines

  1. The time allowed for the contest is one hour.
  2. The use of calculators is not permitted.
  3. Contestants may not consult notes or books during the contest.
  4. Correct answers will be awarded one point. Incorrect or omitted answers will be awarded zero points.
  5. Contestants should be advised to bring a HB pencil for filling out the answer sheet, and paper for roughwork. Only the answer sheet should be handed up.
  6. It is advisable to schedule a few minutes before the commencement of the contest for instructions on filling out the answer sheets and distribution of PRISM ID numbers.

What happens next?

Results of PRISM will be posted by PRISM ID number on this website when they become available. For this reason participants should be advised to retain their ID numbers. The best student (in each category) in each school will receive a certificate documenting the achievement. The outstanding contestants in the country will be invited to an awards ceremony later in the year.
Students who score highly in PRISM will be invited to further develop their problem solving skills through a mathematical enrichment programme at NUI Galway, NUI Maynooth, UCC, UCD or UL. Successful participation in one of these programmes will entail regular attendance at lectures and problem-solving sessions at one of these centres, as well as extensive independent practice at problem solving, supported by correspondence with mentors. Participants in the enrichment programmes usually expect to compete in the Irish Mathematical Olympiad which takes place in early May. This contest involves ten tough problems covering a range of advanced mathematical concepts, and the format is written answer rather than multiple choice. The top six contestants in the Irish Mathematical Olympiad are invited to form the Irish team for the International Mathematical Olympiad (IMO). The IMO is a major international event held annually in July. IMO 2006 was held in Slovenia and 90 countries took part; IMO 2007 will be in Vietnam. For IMO problems over the years, see this site. Ireland's participation in the IMO began in 1987.
Although only six competitors can represent any country in an IMO, it must be emphasised that the process, beginning with PRISM and leading to the Irish Mathematical Olympiad and IMO participation, is for all interested students and is a worthwhile experience in itself. Its purpose is to give participants the opportunity to discover the thrill of problem solving, be it the surprise of a sudden flash of insight or the enduring satisfaction of reaching a solution after a sustained effort.

Organising Committee

The organising committee of PRISM consists of
  1. Dr James Cruickshank, Department of Mathematics, NUI Galway.
  2. Dr Mark Dukes, School of Mathematical Sciences, UCD.
  3. Gordon Lessells, Department of Mathematics and Statistics, UL.
  4. Dr Rachel Quinlan, Department of Mathematics, NUI Galway.
  5. Dr Richard Watson, Department of Mathematics, NUI Maynooth.

For Further Information . . .

. . . keep an eye on this website, which will be updated regularly. If you have a specific query, contact either James Cruickshank or Rachel Quinlan at NUI Galway.