The Scottish Mathematical Council

MC homepage:

The Scottish Mathematical Council

MC homepage:




1. Mathematical Challenge is a problem-solving competition open to pupils educated in Scotland. The aim of the competition is to promote mathematics as a source of interest and pleasurable achievement through challenging problems requiring for their solution only simple techniques and logic. The competition was introduced in 1976 for pupils at secondary school level. As the Scottish Mathematical Council recognised that there are younger children in upper primary who would benefit from the challenge of confronting interesting mathematical problems pitched at an appropriate level of difficulty, the primary competition was introduced in 1994.

Please ensure that all teachers involved in the competition see these Guidelines.

2. Three sets, each of three problems, will be available for downloading from the documents website, according to the timetable in §11 overleaf. The problems will also be available on the Mathematical Challenge Web pages. Pupils will have a month or more to attempt the problems and schools must send their solutions to be received by the local section organiser by the prescribed date. The local organiser's name and address are given on the first page of the documents website above and in the Contacts section of the Web pages.

3. A registration fee is normally payable by participating schools. For a primary school the fee is £8 for the first 10 entrants and half this amount for each subsequent batch of 10 entrants or part thereof. A fee form is included with the downloadable pack of materials.
For individual participants NOT entering through a school, the fee is £8.

4. Solutions must be the unaided efforts of the individual pupil. No help should be given by teachers, parents or others except to encourage clear explanation of how the problem was solved. It is assumed that pupils, in the normal course of their mathematics class work, will have met and practised a range of suitable strategies for solving problems. The work for the competition should be undertaken in the pupils' own time. Group working is NOT appropriate in Mathematical Challenge. Teachers are free to use past problems over a wider range of ages and abilities to suit their classroom practice.

5. Entrants are allowed to use a calculator. No problems set in Mathematical Challenge require the use of a computer package (e.g. a spreadsheet) to obtain a correct solution. If computer software is used, then a proper mathematical explanation of its use is essential.

6. The competition is aimed at the more able mathematics pupils in the upper primary classes. Please be aware that a large number of entries from one school can impose a considerable strain on the organisation and marking of the competition. Teachers should therefore exercise their judgement to avoid the submission of totally inadequate entries. Note that batches of essentially identical entries are not acceptable, and will be returned unmarked.

7. At the top of page 2 of each problem sheet there is a proforma for the entrant's name, school and year. Photocopies of this should be used when submitting the entries. Solutions should be on A4 sized paper and stapled in the top left hand corner. Plastic wallets or other covers should not be used. Entries will not be returned.

8. The marking scheme for each problem is as follows:

4 : a completely correct solution, with full explanation.

3 : a solution, with explanation, which is correct apart from minor omissions.

2 : an attempt which contains ideas towards a solution (with explanation) but not necessarily solving the problem.

1 : an indication of an interesting idea or method, but not necessarily one which could lead to a correct solution.

Explanations which show the pupil has gained some insight into the problem will gain credit even if the solution is not correct. A solution without any explanation will be given no credit, even if the answer is correct.

9. All Sections use a software package to assist in the processing of the results. A Record of Entries must be made electronically by the school, or it will not be possible to process the results.

Use a paper copy of the ‘Printable version of details and entrants’ from the marks website as a cover sheet for the school's entries. This contains the school details and the alphabetical list of entrants in each section, as entered on the website. All entries submitted will be marked even if earlier problem sets are missed.

10. There are three classes of award: Gold, Silver and Bronze. Award winners will be selected on the basis of their performance in the solutions submitted. To win an award it will normally be necessary to submit entries to all three sets of problems.

11. The competition timetable for 2018-2019 is as follows:

Set No.
Last date for receipt
of questions by schools
Last date for receipt
of solutions from pupils
I Friday 24 August 2018 Friday 28 September 2018
II Friday 19 October 2018 Friday 23 November 2018
III Friday 11 January 2019 Friday 8 February 2019

12. The problems of earlier sessions form an excellent resource.

Primary Mathematical Challenges was published by The Scottish Mathematical Council in April 2002. It contains all the problems (with full solutions) which have been offered to primary schools since their initial involvement in 1994-1995 up to the 2000-2001 academic year as well as some problems from the Junior Division. Copies can be obtained from Bill Richardson, Kintail, Longmorn, Elgin, IV30 8RJ, price £5 (inc. p & p.).

In addition, it seems unlikely that any further books will be printed so questions and solutions for 2006-2011 can be accessed at:

Comments on the usefulness of these to would be welcome.

For the secondary competition, the books Mathematical Challenges III, Mathematical Challenges IV, Mathematical Challenges V and Mathematical Challenges VI contain all problems (with full solutions) used in the years 1994-1995 to 2005-2006. These are also available at £7.50, £8, £8 and £8 (respectively).

13. If you have any questions to ask or points to make about the competition, please contact the local organiser for your section, whose name and address are given in the Contacts section of the Mathematical Challenge Web pages

as well as on the materials download menu page