UKMT Challenges


Do not login until the invigilator tells you to do so.

When you log in the system will ask you for your name. Please enter your name carefully. After entering your name click save and then click on the 'Challenges' header. Then select your year group to start the Challenge.

The challenge lasts exactly 60 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 am done' option beneath question 25.

You are allowed only blank or lined 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. Note that there is no penalty marking, unlike previous JMCs. Thus an incorrect answer scores zero.

Questions Correct Unanswered Incorrect
1-15 5 0 0
16-25 6 0 0


The questions on this paper are designed to challenge you to think, not to guess.

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.

Good luck!