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Numbered Graph

Age 16 to 18
Challenge Level

A numbered graph consists of a set of numbered nodes connected by edges. The node sum at a node is the sum of the number at the node and the numbers at all adjacent nodes.

Can you arrange the numbers 1 to 11 on the graph below, using each number exactly once, so the the node sum is the same at each node?

Did you know ... ?

The notion of the mathematical graph is fundamental in modern mathematics and a huge subject of study in its own right. Many systems can be represented by graphs, the internet being a somewhat complicated example. Graph theory is both a fascinating area of pure study and a powerful analytical tool.