The 2026 Junior Maths Olympiad is this week, so today’s problem is inspired by a question from a previous year’s paper. Best of luck to anyone taking part in this year’s JMO!
Vanessa is a vet. Vanessa spends most of her time working at the aviary, but once a week she walks to the zoo across town to tend to the animals there.
Vanessa’s town is built on a grid system, with square blocks and paths that go either North-South or East-West, as shown in the diagram below. The town has a lovely lake right in the middle.
The black dots indicate the entrances to the aviary and the zoo.
The shortest distance between the aviary and the zoo is 10 blocks (where a ‘block’ is the length of the sides of each square). Vanessa likes efficiency (so she never chooses a route that’s longer than 10 blocks) but she also likes variety (so she never repeats the same route twice).
How long does it take for Vanessa to try out every route from A to Z?