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Combinatorics Difficulty 1.2 Junior Find the answer Canada

The town of Cans is north of the town of Ernie. The town of Dundee is south of Cans but north of Ernie. The town of Arva is south of the town of Blythe and is north of both Dundee and Cans. The town that is the most north is

Pick one

Solution

Since Cans is north of Ernie, then Ernie cannot be the town that is the most north.

Since Dundee is south of Cans, then Dundee cannot be the town that is the most north.

Since Arva is south of Blythe, then Arva cannot be the town that is the most north.

Since Arva is north of Cans, then Cans cannot be the town that is the most north.

The only remaining possibility is that Blythe is the town that is the most north.

The following arrangement is the unique one that satisfies the given conditions:

Blythe

Arva

Cans

Dundee

Ernie

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.