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3. Challenges & Competitions

The Scottish Mathematical Council Challenge

Mathematical Challenge is a problem solving competition for individual pupils in Scottish secondary schools and upper primary schools (mainly P7).  It has been running since 1976 under the aegis of the Scottish Mathematical Council . The aim is to promote mathematics as a source of interest and pleasurable achievement.

The competition is divided into four divisions: Primary (P7), Junior (S1 and S2), Middle (S3 and S4), and Senior (S5 and S6).  Each year there are two rounds of problems for Secondary schools and three rounds for Primary schools. The problems and associated documents should be downloaded (click here). Registration of entries and return of marks will be done electronically using the website . Instructions for using this are given in the Guidelines in paragraph 6 for Secondary schools and paragraph 9 for Primary schools.

In early summer winners of Gold, Silver and Bronze Certificates are announced in each section;  the top winners are usually invited to a prize-giving ceremony and receive a much prized Mathematical Challenge mug.

Marks are given for explanations of answers rather than for simply getting the correct answer.


The UKMT run a series of mathematics challenges to encourage children's interest in mathematics and develop their skills:

  • Junior Mathematical Challenge (S2 and below)
  • Intermediate Mathematical Challenge (S4 and below)
  • Senior Mathematical Challenge (S6 and below)

In the Junior and Intermediate Challenges the top scoring 40% of the entrants receive bronze, silver or gold certificates based on their mark in the paper. In the Senior Mathematical Challenge these certificates are awarded to top scoring 60% of the entries. In each case bronze, silver and gold certificates are awarded in the ratio 3 : 2 : 1. So in the Junior and Intermediate Challenges

  • The Gold award is achieved by the top 6-7% of the entrants.
  • The Silver award is achieved by 13-14% of the entrants.
  • The Bronze award is achieved by 21% of the entrants.

For the Senior Challenge these percentages are 10%, 20% and 30%, respectively.

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