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An intriguing problem that challenges students to visualise different possibilities.
And when they have found one solution they can be encouraged to find more...

Older students who have been introduced to trigonometry might like to use the relationship between the circumference of a circle and its radius to estimate/calculate how far Bilbo's home is from the poles?

For this they may find it useful to know that the circumference of the earth is about 24,900 miles, and the radius of the earth is about 3,960 miles.