Total Totality
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?
Age
11 to 14
Challenge level
This network has nine edges which meet at six nodes. The numbers $1$, $2$, $3$, $4$, $5$, $6$ are placed at the nodes, with a different number at each node. Is it possible to do this so that the sum of the $2$ numbers at the ends of an edge is different for each edge?
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Either show a way of doing this, or prove that it is impossible.
More Total Totality is a follow-up short problem to this one.
More Total Totality is a follow-up short problem to this one.
The task is possible to do as shown.
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