Team Competition

The 9th ICMC Team Competition

Solve mathematical problems and puzzles with your friends at the Imperial–Cambridge Team Mathematics Competition! Competing as teams of five, contestants will be challenged with five rounds of puzzles – Functions, Shuttle, Relay, Crossnumber, and Quizdle. This year, the details are as follows:

Date: Sunday, 22nd February 2026, 15:30–18:00
Venue: Huxley Building, Imperial College London

How to register

Register your interest for the Team Competition

Registration Deadline: Wednesday, 11 February, 23:59 (UTC time).

If you would like to participate in the Team Competition, and do not care too much about who is in your team, you can register as an individual/partial team and we will try to match you up with other partial teams. In doing so, we will try to match up partial teams with other partial teams of similar mathematical ability.

You will be notified about whether your team/partial team has been accepted at latest by 12 February.

Details

Each team consists of five people. There will be five activities, and for each activity each team will need to appoint a different member who will act as the marker for another team.

Please note that due to space constraints, we may not be able to accept every team that registers. Priority will be given to teams with a higher number of Round Two qualifiers, a higher number of students from underrepresented universities, and teams representing a single university. Teams consisting of three or more Round Two qualifiers will be guaranteed entry, although we still encourage you to register even if no members of your team are Round Two qualifiers.

Eligibility

To be eligible for the competition, you must:

be a current bachelor's or master's student,
be enrolled at an institution located in Europe (for our purposes this includes Turkey and the areas of Russia observing Kaliningrad Time or Moscow Time), and
have participated at most four times previously in the Team Competition.

All students are welcome to participate regardless of their area of study.

Format

The competition will consist of five activities: Functions, Shuttle, Relay, Crossnumber, and Quizdle, in that order. For examples of each of the activities, please check our past papers. As mentioned above, for each activity each team will need to appoint a different member to act as the marker for another team. The marker will receive an answer sheet which will contain further instructions about marking.

Functions (20 mins, 30 points)

There are five mystery functions, and your goal is to figure out what they are. Each team will be able to make up to ten queries regarding the output of the functions. For each query, the marker will write down the function's output. The first five queries are "free", and guessing the function correctly within five queries gains the team 6 points. Each query thereafter costs 1 point. The functions are generally ordered by difficulty, but they do not have to be worked on in order. Teams may try the functions in any order, and may come back to functions later.

Shuttle (24 mins, 36 points)

Each team works as pairs of two in this round. From a set of 4 questions, one pair will be given the first and third questions, and the other the second and fourth questions. The answer to the first question will be required for the other pair to fully know what the second question statement is, and similarly for the second and third questions. However, the problems are formulated so that it is usually possible for each pair to reach a partial solution independently. The two pairs are not allowed to communicate on any matters related to the questions themselves, but may encourage the other team to, for example, hurry up or make a guess before time runs out.

Two attempts are allowed for each question – four points are awarded for a correct first attempt, and two points are awarded for a correct second attempt. After two failed attempts, no points will be awarded, and the referee will pass the correct answer to the pair working on the next question. There will be two sets of questions, with 12 minutes for each set. Two bonus points will be awarded to teams who finish faster than 8 minutes, and one to teams who finished faster than 10 minutes.

Relay (20 mins, 28 points)

Six 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). Getting a question correct on the first attempt is worth 4 points, and getting a question correct on the second attempt is worth 3 points. Teams will get 20 minutes for all six questions, but teams that finish in under 16 minutes will get 4 bonus points, while teams that finish in under 18 minutes will get 2 bonus points.

Crossnumber (20 mins, 30–35 points)

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.

A pair of contestants may submit their answers to the clues in any order. Answers cannot begin with leading zeros. Squares can and should be attempted individually, with one point awarded for each correct and previously unattempted square. One attempt is allowed for each square. Each pair is responsible for copying the correct answers into their own copy of the crossnumber grid. Answers provided by the down clues team may be helpful or necessary for an across clue to be solved, and vice versa. The two pairs are not allowed to communicate on any matters related to the questions themselves, but may encourage the other team to, for example, work on a specific clue.

Quizdle (20 mins, 30 points)

The rules are similar to Crossnumber, described above, except that the questions will ask about a range of mathematical trivia and the answers will be words or names. One difference is that the clues must be attempted as a whole, not letter by letter. One other major difference is that there will be three sets of clues. Each set of clues will clue the same answers, but they will contain either hard, medium, or easy clues. At the start of the activity, both pairs will start with the hard set of clues, where each correct answer is worth 1.5 points. At any point, the team may ask for the medium set of clues: each correct answer is now worth 1 point. At any point, the team may ask for the easy set of clues: each correct answer is now worth 0.5 points. Note that Across answers will not be necessary for the Down answers and vice versa, unlike in crossnumber. Each answer can only be attempted once, regardless of whether the hard, medium, or easy clue was used.

At the end of the round, a team's score will be rounded up to the nearest integer.

Learn more

If you have any further enquiries, please contact us at enquiries@icmathscomp.org.