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Counting on Letters

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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Medal Muddle

Stage: 3 Challenge Level: Challenge Level:1

Thank you to everyone who participated! The correct answers, which almost everyone got, were:

1. Russia

2. France

3. Algeria

4. Serbia

5. Turkey

6. Greece

7. Portugal

8. Mexico

9. Venezuela

10. Italy

11. New Zealand

12. Spain

13. Romania

Congratulations if you got the order right! Let's have a look at some of the ways of doing it.


Alex, from Winnersh Primary School, had the following interesting idea to find the countries in order, one at a time:

My method was to choose a random country and then go through the clues until I found a country that was higher up. I carried on until I found a country where I could go all the way through the clues without finding another one that was higher up. I then put that country (Russia) in 1st place. I would then do the same but ignoring Russia, and found the 2nd, then 3rd, etc.

Rebecca, from Woodchurch, had a similar idea:

Try to count how many times one country came above each other country. Then repeat this thirteen times. Then put your answers in order. Ta-da!

Daniel, from Wilson's School, wrote down at each step what he got from the hints:

From hint 1, you can get:

  • Turkey / Mexico
  • Italy / New Zealand

From hint 2, you can get:

  • Portugal
  • Venezuela / Mexico / Spain / Romania

From hint 3, you can get:

  • Greece / Spain / Serbia / Algeria
  • Romania.


Many people thought it was a good idea to write the names of countries on bits of paper or card and swap them round - this saves a lot of writing! For example, Michelle, from Globe Academy, wrote:

I started by putting the country names in a random order. Then I read through the clues and started swapping around the countries. When I got to the end of the clues I went back through the clues and checked again.

Mrs. McGuire's class at Lakewood Catholic Academy were another one of many who followed this approach - they say it took them about 45 minutes and lots of trial and error. Could it have been speeded up, do you think?

Jade, at Oakmeeds, sent us the following comments on the card idea:

I wrote some of the infomation to do with the country on the country's card, e.g. "above Spain and Algeria and below New Zealand".


  • Easy to read and clear
  • Enjoyable when arranging the cards
  • Pretty quick if you have an idea in your head
  • Makes you happy when you complete it!


  • The writing process is slightly tedious


  • When writing the notes on the cards write short phrases and clearly so easily read.
  • If you write the wrong infomation on the cards then it's not going to be pretty...

Charlie, from Wentworth Primary, had this interesting idea:

I used a mathematical method allocating points for each one above and subtracting a point for below, to eventually work out where each country should go by adding up the points I had allocated.

Mrs. Gale's class, from Churchill Academy, had a trick to speed things up slightly:

Colour coding the countries to make them stand out more easily. This made it clear there was most information about France.

On a similar note, Alastair from Richmond CoE sent us lots of flags that he printed out and cut up while constructing his solution. Nice!

A few people moved onto the extension problem using the same sorts of techniques as above. The correct answer was:

Sri Lanka,  Great Britain, Brazil, Spain, Turkey, Austria, Romania, Finland, Mexico, Germany, Serbia, Italy, Canada, Algeria, New Zealand, Australia, Norway, France, Portugal, Greece, Japan, Sweden, Venezuela, USA, Russia, Denmark.

Thanks to Brain Academy at St. Peters CEVC Primary, Mrs. C's class at Court Moor School, and Ms. Troup's class at Prior's Field School for sending in their answers to the extension problem - this one was tough!

(Finally, Stefan from Afghanistan said: "this is so cool"! Thanks, Stefan!)