Stage: 4 Challenge Level: 
Why do this problem?
In this problem learners have to identify the mathematical features of the context and represent these features in graphical and algebraic forms. They will get practice in analysing and mathematical reasoning through using algebraic expressions and equations to find solutions. In order to check that they have found all possible solutions learners need to work systematically and check all possible cases.
Possible approach
This is essentially the same problem as W. Mates and there you will find the first steps for solving this problem. Then the problem Magic W Wrap-Up gives more ideas for solving the same problem.
Key questions
What is the sum of the whole numbers 1 to 9?
If the total in each circle is Xwhat can you say about the total of thenumbers that are in the intersections of the circles?
Networks/Graph Theory. Working systematically. Combinatorics. Algorithms. Complex numbers. Making and proving conjectures. Games. Codes and cryptography. Interactivities. Mathematical reasoning & proof.
Published March 2003,August 2008.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk