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### Number and algebra

### Geometry and measure

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### Working mathematically

### For younger learners

### Advanced mathematics

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Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

- Problem
- Student Solutions

You can draw 1, 2, 3, 7, 8, 9 and 11 without taking your pen off the paper.

**Why?**

Nodes are places where two or more lines meet. On these diagrams, the nodes are clearly shown by the black points.

If a node has an even number of lines coming from it, this means that your pen will be able to both enter and leave that node.

If not, the pen must start or finish at the node.

As you can start and finish at only two nodes (start at one, finish at the other), if the diagram has more than two nodes with odd numbers of lines, you won't be able to draw it without taking your pen off the paper.

If all the nodes have even numbers of lines, then you can draw the diagram without taking your pen off the paper and starting and finishing at the same place.