# Team Competition

## The 7th ICMC Team Competition

Solve mathematical problems and puzzles with your friends at the Imperial College 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, 25th February 2024, 15:30–18:00
- Venue: Huxley Building, Imperial College London

### How to register

**Register your interest for the Team Competition

Registration Deadline: Thursday, 15 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.

You will be notified about whether or not your team/partial team has been accepted at latest by 16 February.

### Details

Since the 6th ICMC, the team size has been 5 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. This change is due to an expected increase in the total number of teams, and the difficulty in obtaining one volunteer marker per team.

As an advanced warning: 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. 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 an undergraduate or master's student who has completed less than four years of university education. Students from all subject areas are welcome.

## 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 also contain further instructions about marking (these are not contained in previous Team Competition solutions pdfs).

### Functions

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, and they must be worked on in order.

This activity lasts 20 minutes, and is worth 30 points in total.

### Shuttle

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.

There will be two sets of questions, with 12 minutes for each set. The activity is worth 36 points in total.

### Relay

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.

This activity lasts 20 minutes, and is worth 28 points in total.

### Crossnumber

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 be attempted individually, 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 square. 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.

This activity lasts 20 minutes, and can be worth between 25 to 35 points, depending on the number of squares in the crossnumber of a given year.

### Quizdle

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. 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 2 points. At any point, the team may ask for the medium set of clues: each correct answer is now worth 1.5 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 and Down answers will not depend on each other like they do 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.

This activity lasts 20 minutes, and can be worth between 28 to 40 points, depending on the number of clues.

## Learn more

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