Past Papers


Team Competition

Solve mathematical quizzes with your friends at the Imperial College Team Mathematics Competition! Competing as teams of four, contestants will be challenged with four rounds of puzzles — free group, shuttle, relay and crossnumber.

Date: Sunday 23rd February, 14:30 – 16:30
Venue: Clore Lecture Theatre, Huxley Building

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Eligibility: To take part in the Competition, you must be either
a) a current undergraduate student, or
b) a current master's student who has received less than four years of university education.

Below are tentative descriptions of the four rounds, with sample questions for the shuttle and crossnumber rounds.

Free group

A collection of warm-up questions, with a time limit. Contestants are free to discuss the questions within their team.


Each team work as pairs of two in this round. From a set of 4 questions, one pair will be given the 1st and 3rd question, the other the 2nd and 4th. Although it is usually possible for each pair to reach a partial solution independently, to fully solve each of the latter 3 questions a pair will need the answer to its preceding question from their teammates. Teams are not allowed to talk across the pairs except via the referee assigned to the team.

Two attempts are allowed for each question, with fewer points available after a failed first attempt. After two failed attempts, the referee will pass the correct answer to the pair working on the next question. There is a time limit; bonus points are awarded to teams who finish a set of questions sufficiently faster than the time allowed.

There will be two sets of questions. Here is a sample set.


A (finite) sequence of questions are available, but teams will only be given a new question after they have solved the one they are working on (or have failed to reach the correct answer after two attempts).


The "crossnumber" grid is similar to a crossword puzzle, but each square is to be filled in with a number and the clues are maths questions. Teams are asked to split into pairs again, with one pair receiving the "across" clues and the other "down" clues. Again, one pair may only communicate with the other pair via the referee and a time limit is imposed.

A pair of contestants may submit their answers to the clues in any order. All squares corresponding to any single clue must be attemped as a whole, with one point awarded for each correct and previously unattempted square. The referee will then pass the correct answers to the entire clue to the other pair. One attempt is allowed for each clue. Answers provided by the down clues team may be helpful or necessary for an across clue to be solved, and vice versa.

Here is a sample crossnumber puzzle, which featured in the 2019 Team Competition.

Individual Competition

Round One took place on Sunday 24 November at Imperial College London and our partner universities. The problems and solutions have been posted on the past papers page.

Round Two

Contestants with the best Round One results will be invited to Round Two, which is currently scheduled to take place at Imperial College London and Australian partner universities on Sunday 23 February. We may be able to partially reimburse travel expenses and details will be announced to invitees in due course.