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'There and Back Again' printed from https://nrich.maths.org/
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.