Live Problems

We often have a selection of 'live problems' on the site which are open for solutions on the Primary live problems and recent solutions page and Secondary live problems and recent solutions page. This means we are inviting students to send in thoughts, ideas, workings out and solutions, and then we'll publish a selection of them. Each of these problems has a 'Submit a solution' tab which you can click on to submit your solution. The other problems on the site generally already have published solutions, and we aren't usually accepting new solutions to these problems.

We publish solutions that are clearly explained so that students, teachers and parents can use them to see how a problem can be solved.

We receive solutions in a variety of formats. Here are a few examples:

• Emily and Niharika's handwritten and scanned solutions to Opposite Vertices
• The spreadsheet that Susan sent for her solution to Constructing Triangles
• George and Sophie's photo of their completed Fraction Jigsaw
• The video that Martha made in response to Perception versus Reality

Answer or Solution?

The first decision we make is whether a solver has sent us an 'answer' or a 'solution'. An answer is brief and just contains answers to the questions we've posed. A solution may not be complete, but will include the solver's ideas, why they chose a certain method, and explanations of what they noticed. We want someone looking at the published solution to get some understanding about the sort of thought processes that led to the answer, so they can learn from someone else's work and become a better problem-solver.

Mathematically Correct

Next, we need to make sure that the solution is mathematically correct. If there are one or two minor errors, we will correct them and publish the solution, but if a solution shows a major misconception or the solver didn't really explain their method, we won't publish this solution. If a solution began very clearly but had lots of errors towards the end, we might publish just the first part of that solver's work.

How we organise solutions

We start by looking for solutions that tackle just the first part of the problem and we tend to publish these at the top of the page. We then build up a full solution, often by piecing together several partial solutions, focusing on showing different approaches to a problem and the different layers of thinking required. We try to order the solutions to reflect increasingly sophisticated methods - we don't want to put anyone off having a go at the problem, which is why solutions using higher-level mathematics come nearer the bottom of the page. Occasionally we will publish an entire solution as an additional download, especially where this involves a lot of deeper thinking about the problem.

Tips for students on how to get your solutions published

1. Check your solution carefully, and perhaps ask someone else to look over it to spot any mistakes you might have missed.
2. Explain simply and clearly what you did to solve the problem. It doesn't have to be a long explanation, but we like solutions that share the mathematical journey of the solver.
3. If you made any diagrams or used a spreadsheet to help you, upload it with your solution. Make sure you explain clearly what you are referring to if you talk about your diagram or spreadsheet in your solution.
4. If you upload your solution as a document, keep it as simple as possible. If you send a solution with lots of formatting, your solution might not appear on our screens as you intended. If you use a less common file type, or if you send a link to your solution somewhere on the internet, we might not be able to open it. Word documents and PDF files are fine.
5. Read through other people's solutions to previous problems on the site. This will give you a flavour for the sorts of solutions we publish, and help you to develop your own mathematical style for writing up your work. Learning how to communicate mathematically is an important part of learning to be a mathematician!