[GeoffC]

Originally Posted by omk3

Spoiler:

But the key information is that they know it is either 1 or 3, never 2. So both seeing 1 is not possible. They would never be free if they didn't know the towns are either 10 or 13. But this information changes everything.

this post was specifically directed at Sparrow's scenario.

Spoiler:

East sees 1 town, but doesn't know whether West sees 0 or 2.

West sees 0 towns, but doesn't know whether East sees 1 or 3.
West knows that if East sees 3 he would have used the get out of jail card.
West holds all the clues and can answer 1.

It works for the small number scenario, but when the numbers increase