This activity presents an exercise in strategic thinking, accessible to lower secondary students (but hinting at the more advanced mathematics of sorting algorithms that they might meet if continuing to study maths at A-level). It is aimed at Key Stage 3 students.

Detailed teachers' notes for this activity are available on our NRICH website.

Medal Muddle

Stage: 3 Challenge Level: Challenge Level:1

If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...


Thirteen nations competed in a sports tournament. Unfortunately, we do not have the final medal table, but we have the following pieces of information:

1. Turkey and Mexico both finished above Italy and New Zealand.

2. Portugal finished above Venezuela, Mexico, Spain and Romania.

3. Romania finished below Algeria, Greece, Spain and Serbia.

4. Serbia finished above Turkey and Portugal, both of whom finished below Algeria and Russia.

5. Russia finished above France and Algeria.

6. Algeria finished below France but above Serbia and Spain.

7. Italy finished below Greece and Venezuela, but above New Zealand.

8. Venezuela finished above New Zealand but below Greece.

9. Greece finished below Turkey, who came below France.

10. Portugal finished below Greece and France.

11. France finished above Serbia, who came above Mexico.

12. Venezuela finished below Mexico, and New Zealand came above Spain.


Can you recreate the medal table from this information?

Can you describe an efficient strategy for solving problems like this?



The following year, twice as many teams entered the tournament. Can you use your strategy to sort out the medal table from these clues?


Perhaps you might like to try creating a similar problem of your own.

You will need to consider the following:

Although there are twelve statements above, there are more than twelve pieces of information, because some sentences compare more than one pair of teams.

What is the minimum number of pieces of information needed to order the teams?

Which information, if any, is redundant?



Further information

If you're finding hard to get started, try looking at this hint.

Detailed teachers' notes for this activity are available on our NRICH website.