Stage: 3 Challenge Level: 
There are 30 students in a class and it is found that in any subset
of 4 students from the class each student has exchanged Christmas
cards with the other three. Show that some students have exchanged
cards with all the other students in the class. How many such
students are there?
Pythagoras' theorem. Generalising. Comparing and Ordering numbers. Visualising. Patterned numbers. Mathematical reasoning & proof. Number - generally. Creating expressions/formulae. Number theory. Combinatorics.
Published December 1998.
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