Problem Solving Competition

Win a copy of Simon Singh's "The Simpsons and their mathematical secrets" and a £50 Amazon voucher

Can you solve this vexing vexillology problem?

You are asked to make flags for an event. The attending nations are Nepal, Japan, Czech Republic, South Korea, Bahrain, Bangladesh, and the Philippines.

  • They must be mathematically accurate.
  • They must all be 1.2m in height.
    (You can ignore the blue border when calculating the height of the Nepalese flag.)
  • Each piece of a single colour must be a single piece of fabric
    (i.e. cannot be made of multiple pieces of fabric put together).

The fabric you use is on a roll of 2.4m wide. You notice you only have 2m left on the roll of RED material.

  1. What flags can you make to produce the least wasted material, and how much material is wasted?
  2. What length of additional material would you need to make the remaining flags?
  3. What is the smallest length of this fabric that would allow you to make all the flags of this size?


  • The prize is a copy of Simon Singh’s “The Simpsons and their mathematical secrets” and a £50 Amazon voucher.
  • You must be in Years 7 to 11 to enter.
  • You can download the questions here.
  • You need to submit the completed answer sheet; make sure it contains your name and school so we can contact you if you win. Please ensure this is written clearly as if we can’t identify which school you attend we may not be able to contact you if you win.
  • Entries must be received by 1st February 2019.
  • If more than one correct entry is received then the winner will be drawn from a hat on the 4th February.
  • The winner will be notified in February via their teacher.
  • The school and winner will each receive a certificate.

To enter

  • Entries should be emailed from a teacher’s school email account to [email protected] to be received no later than noon on 1st February 2019.
  • Entrants must include their name and school.
  • Multiple entries can be submitted electronically from a teacher’s email account as long as it is clear which student has submitted each answer.
  • Entries can be posted to: Problem Solving Competition, FMSP, Monckton House, White Horse Business Park, Trowbridge, BA14 0XG to arrive by 1st February 2019.
  • Each student may only enter this competition once.
  • Students must be in school years 7 to 11 when the entry is submitted.

If you are struggling to find information on how to make the flags, Wikipedia can be a good place to start.