We can represent a group of friends by drawing a graph.
Each node represents a person.
An edge joins two nodes if and only if those two people are friends.
Here is a graph showing a group of friends.
Can you work out who's who using the clues below?
Here is a second network of friends.
Again, can you use the clues below to figure out who's who?
Once you've solved the two puzzles, here are some questions to consider:
Did each problem have a unique solution?
Were there any clues you didn't need to use?
If you label each node with the number of friends the person has, and add together all the numbers, what can you say about the answer? Can you explain why?
Can you design a puzzle which has a unique solution?
Can you design a puzzle which has two possible solutions?
Have a go at creating some other friendship network puzzles of your own and send them in for us to try!
Download a printable version of this problem
This problem featured in an NRICH Secondary webinar in September 2021.