# Ritangle

Ritangle is a competition designed for teams of students aged 16‌-‌18 who are currently studying either:

• A level Mathematics
• the International Baccalaureate
• Scottish Highers
• qualifications with equivalent content.

No knowledge of maths beyond A level Mathematics is expected.

9 weeks

29 questions

1 winning team

Students who take part are so engaged and excited by it, every year. They live and breathe it for the duration. And they learn so much from being involved in it.

Maths teacher

## How does it work?

Registration

from 3 October

Teams can register for this year's competition

Stage 1 questions

3 October - 5 December

For the first four weeks, one question is released every Monday. For the following 5 weeks, three questions will be released on Mondays, Wednesdays and Fridays. The final question of Stage 1 will be posted on Monday 5 December.

Every correct answer reveals a piece of information that helps solve the Final Task.

6 December, 16:00 (GMT)

Final challenges released.

Use the information you've gained from solving the previous questions to reveal new challenges and solve the Final Task.

13 December, 16:00 (GMT)

## What can we win?

A maths hamper, containing a mix of prizes for individual team members and their school. It includes a free year-long subscription to Integral, and a trophy for the school or college of the winning team!

## Using technology

The Ritangle rules state: “Any help with the questions is permitted, including finding information about the questions on the web and using technology.”

You may have never used technology to solve a mathematical problem before but it can be extremely helpful - it can illuminate aspects of the problem that you may not have otherwise noticed and it can be great fun.

Technology can certainly help with some of the questions in Ritangle. This can range from using spreadsheets, to using graphing software, right the way through to coding. You might also find Computer Algebra Systems useful - these can perform algebraic processes in the same way that calculators carry out arithmetic.

### Approximating Roots of Equations

Using GeoGebra and Desmos to approximate roots of equations

Finding approximate solutions to equations using a graphing calculator

A spreadsheet, which can be programmed with Visual Basic

Using Excel to solve a problem involving the digits of numbers

Introduction to programming Excel using Visual Basic

Graph plotter, spreadsheet, general mathematical calculator, Computer Algebra System, programmable

Programming language

### Getting started with MATLAB

Promote the competition to your students

Creative, challenging, innovative - Ritangle nurtured teamwork, enthusiasm, resilience. Absolutely loved it.

Maths teacher

## Questions from previous years

If you are looking for problems and solutions from previous years' competitions, follow the links below:

### General

Ritangle is a free maths competition aimed at teams of sixth form/ college students running from early October to mid-December. The ‘Stage 1’ questions are released one at a time across this period; the answers unlock information to solve the final multi-part question.

Stage 1 questions can be viewed on the Integral Twitter feed and registered teams can access them through their team login.

The final question is available only to registered teams through their team login.

Students studying A level Mathematics/Further Mathematics, Scottish Highers or International Baccalaureate anywhere in the world.

Ritangle is pronounced like ‘right angle’ or ‘wry tangle’.

### Registration

One student from the team must register the team. The team should agree who this will be to ensure there is only one entry per team. This student is the Team Captain. Every student can only be in one team, including the Team Captain. Once registration opens, you'll be able to do so on the Ritangle webpage and a team must be registered in order to submit answers.

• School/college name
• Team Captain's name
• Nominating Teacher's name

There is no limit to the number of members a team can have but we suggest about 4 or 5 so all members can be actively involved.

No, all students in a team must attend the same school/college

Yes, there is no limit to the number of teams a teacher can be a Nominated Teacher for.

No, each student can only be in one team, including the Team Captain.

### Taking part

Rules will be published at the start of the competition.

Please note: anyone found leaking the answers or clues inappropriately and anyone found making intentional use of such leaks will be disqualified from the competition.

Yes! We encourage the use of technology; spreadsheets, graphing software and programming can be particularly useful. Any use of online resources/search engines is also permitted.

When we explore maths for ourselves these days, we may have a spreadsheet, a graphing program, a CAS program and a programming environment open simultaneously, and we want Ritangle to have that flavour. We think it is reasonable to expect students to be able to use a graphing program and a spreadsheet. Programming knowledge will not, however, be required for the final question.

On the other hand, we accept that when working against the clock (such as while working on the final task) methods using technology may have outpaced more traditional methods. We bear this in mind when constructing tasks.

Please note: any team repeatedly attempting to use an automated process to systematically enter answers until the correct answer is found will be disqualified from the competition.

It is possible to solve the final question even if you don’t have correct answers to all of the Stage 1 questions. If it is apparent that a question is too difficult, hints may be provided publicly by the Integral team.

This is tricky. We have tried 9:00 (2016–2018 inclusive) but this favours students whose schools are happy for them to go off timetable for part of the day. On the other hand, 16:00 makes life difficult for other students, who may be travelling at that time. Support for each of these start times has been about equal amongst participants.

Our solution is to make the final task harder to complete quickly, so that the winning time lies between two days and seven days. This is a delicate balancing act.

We have considered dropping the race-to-the-line element of the final task, and having a more qualitative task for those scoring fully on the final question. We have decided to shelve this alternative for now.

Yes! Judges may request to see evidence of working out. Answers to questions are also required at a later stage in the competition. We recommend that each team nominates a member as Team Archivist to keep the team’s working for the questions as they are attempted.

We ask that teachers do not help students directly, but any help with relevant theory is fine.

### Winning

Every team that submits a creditable answer to the final question will receive a certificate, emailed to their Nominated Teacher.

The winning team will receive a maths hamper, containing a mix of prizes for individual team members and their school. It includes a free year-long subscription to Integral, and a trophy for the school or college of the winning team. We reserve the right to substitute a prize of equivalent value but of less weight/bulk should the winning team be based abroad

Please note: the following is subject to the team providing sufficient evidence (in the opinion of the judges) of their working.

Answers for the final question will be accepted up until the date published in the Information and Rules document.

Scenario 1
The team scoring most highly on the final question will be declared the winner, subject to their working satisfying the judges.
Scenario 2
If there is more than one team with the highest score on the final question, the winner will be chosen, from such teams, as the team that submitted those answers first, subject to their working satisfying the judges.
Scenario 3
In the event that the above does not determine a winner, the winning team will be chosen at the discretion of the judges based on the answers submitted.

If there is a possibility a team has won, the judges will contact the Nominating Teacher to verify details of the team and their participation. If the answer is satisfactory to the judges then that team will be the winner. The decision of the judges is final. No discussion will be entered into regarding the decision over who is the winner. The winning team and the answers will be announced on this webpage and on the Integral Twitter feed.