Sure, but I will limit myself to one, which is fairly exemplary.

The question is to show that R2 is second countable. This means that it contains a countable base for the topology. The usual way to do this is to pick open balls with rational centers and rational radii, and use a little finesse to find one around any point in an arbitrary open ball.

The Author's answer was to take the set of all open balls, and pick only those with natural number radii. This is neither countable nor a base for the (usual) topology on R2. This answer has a check mark on it.