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Counting on Letters

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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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

You may find it useful to print off and cut out these cards. You could arrange the countries randomly and then read through the clues adjusting the order as you go. Here is a set of cards for the extension.

Alternatively, you could begin by figuring out which teams couldn't have come first.

 

One way of working is to take each clue and turn it into a set of relations between pairs of countries:
"Russia finished above France and Algeria" could be turned into "Russia above France" and "Russia above Algeria".
 
The diagram below can help you draw vectors between pairs of countries, with arrows used to indicate the order in which they finished. (Be patient; the applet may take some time to load.)
 

If the GeoGebra applet does not load correctly you can save the GeoGebra file and open it using the free to download GeoGebra software.