Guidelines

1. Mathematical Challenge is a problem-solving competition which goes back to 1976. The Challenge is open to all students educated in Scotland. Its aim is to promote mathematics as a source of interest and pleasurable achievement through challenging problems which require only elementary techniques and simple logic.

Follow the Mathematical Challenge link on the SMC Web homepage for local contacts, recent problems, current problems and more.

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

2. There are four divisions: JUNIOR for Sl and S2, MIDDLE for S3 and S4, SENIOR for S5 and S6, and PRIMARY (for which a separate circular is available).

Pupils may enter only one division and must specify that division on their first entry.

Please contact your local organiser, whose name and address are on the proforma on page 2 of each problem sheet and in the Contacts section of the Web pages, if there is any doubt about divisions, or if further information is required.

3. There are no written examinations. For the Junior, Middle and Senior Divisions, two sets of five problems each will be sent to schools according to a timetable outlined in §13 below. Problems for different divisions will be on separate sheets. Some problems may be common to different divisions. The problems will also be available from the Mathematical Challenge Web pages (see above for address).

4. A registration fee is required from participating schools. For a secondary school the fee is £12 (for a primary school the fee is £6). For individual participants NOT entering through a school, the fee is £6.

5. Entries must be the unaided efforts of individual pupils. Group working is not appropriate in Mathematical Challenge. Contestants may consult books for information on facts or on how to tackle problems. Whilst teachers or parents may give guidance on interpretation of wording, they should not be involved in the solution of a problem. Furthermore, the work should not interfere with normal teaching and in no circumstances should it be a class assignment.

6. Teachers are requested to enter the names, divisions and school years (i.e. S1, S2 etc) of all their entrants on the Record of Entries forms, which will be provided. These forms will be used to return marks to schools. Entries should be received by the dates given in §13. All solutions submitted will be marked, even where the entrant has missed the first problem set.

7. Entries will not be returned. Entrants should keep a copy of their solutions. The Scottish Mathematical Council reserves the right to publish good solutions in its Journal.

8. Participants should explain their solutions as fully as they can. Marks will be given for explanations of answers not just for the answers themselves. We should be most grateful if teachers would stress this point. Incomplete or incorrect answers may gain some credit.

3 : a solution, with explanation, which is correct apart from a minor slip or omission of a special case.

2 : a solution with explanation which contains a serious error or omission, but which nevertheless involves good ideas

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

A bonus mark may be given for a completely correct solution, with full explanation, which contains additional good ideas, such as a successful generalisation of the problem.

A solution in which an answer is given without any explanation will normally be awarded no marks, even if the answer is correct. However, correct working may be accepted as providing an explanation, so long as the various steps are clear.

9. 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.

10. There are three classes of award: Gold, Silver and Bronze. Award winners will be selected primarily on the basis of the total number of marks obtained over both sets of Problems. Special circumstances for individual entrants may be taken into account.

11. All award winners will qualify for certificates. Where an award ceremony can be arranged, the most successful entrants will be invited to attend to receive their certificates and Mathematical Challenge mugs. Certificates not presented at a ceremony will be sent by post.

12. Large numbers of entries can impose a considerable strain on markers and on organisers. Local organisers may have to set limits on the total numbers of entries per school. Schools submitting large entries may be asked to provide additional markers. Any such markers would not mark entries from their own schools. Large entries received from one school may be returned for resubmission.

*Set No.*	Last date for receipt of questions by schools	Last date for receipt of solutions from pupils
I	28 August 2009	2 October 2009
II	27 November 2009	5 February 2010

14. The problems of earlier sessions form an excellent resource. Those for the years 1991-92 to 2005-2006, including solutions, are available in the books Mathematical Challenges II, Mathematical Challenges III, Mathematical Challenges IV, Mathematical Challenges V and Mathematical Challenges VI which are published by The Scottish Mathematical Council. Copies can be obtained from Bill Richardson, Kintail, Longmorn, Elgin IV30 8RJ, prices £6, £7.50, £8, £8, £8 respectively.

15. For other information, please contact your local organiser, whose name and address are given on the proforma on page 2 of each printed problem sheet, and in the Contacts section of the Mathematical Challenge Web pages.

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.

Follow the Mathematical Challenge link on the SMC Web homepage for local contacts, recent problems, current problems and more. In time, solutions will also be published on the Web pages.

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

2. Three sets, each of three problems, will be sent to schools either via their associated secondary schools, or via the normal local authority distribution service to schools or directly by post, 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 second page of each problem sheet 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 £6 and for a secondary school the fee is £12. For individual participants NOT entering through a school, the fee is £6.

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. Please contact the local organiser if you expect to submit more than a dozen or so entries from your school. 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.

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. A Record of Entries proforma will be provided, on which the names of each entrant and his or her school year should be listed. This form will act as a mark sheet to be returned to the school after the marks have been entered. 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.

*Set No.*	Last date for receipt of questions by schools	Last date for receipt of solutions from pupils
I	28 August 2009	2 October 2009
II	23 October 2008	27 November 2009
*III*	11 January 2010	19 February 2010

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.).

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 on the second page of each sheet of problems and also in the Contacts section of the Mathematical Challenge Web pages:

MATHEMATICAL CHALLENGE 2009-2010