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