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# Eulerian

Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn? Can you explain your reasoning?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

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Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn? Can you explain your reasoning?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?