UKMT Challenges


Senior Mathematical Challenge 2022 Instructions

The challenge lasts 90 minutes. Your clock starts when you click on the start button. You can attempt the questions in any order and your answers will be saved immediately but you can always go back to change an answer. When you are done you can close your browser, logout or select the 'I have finished' option beneath question 25.

Please note that your answers are saved as you go along. Even if you run out of time and the system logs you out, all answers submitted up to that point will have been saved.

You are allowed only blank paper for rough working. Squared paper, calculators and measuring instruments are forbidden.

Do not expect to finish the whole challenge in the time allowed. The questions in this challenge have been arranged in approximate order of difficulty with the harder questions towards the end. You are not expected to complete all the questions during the time.

The following table shows the scoring rules.

All candidates start with 25 marks









The questions on this paper are designed to challenge you to think, not to guess, hence the penalty marking.

You will gain more marks, and more satisfaction, by doing one question carefully than by guessing lots of answers. This paper is about solving interesting problems, not about lucky guessing.

Now get ready to begin the challenge.

Senior Mathematical Challenge 2022 - Scotland S3 or below

During this practice competition you will receive immediate feedback on your answer.

(During the official challenge you will not see whether you have answered a question correctly or not.)