[omk3]

Originally Posted by GeoffC

this post was specifically directed at Sparrow's scenario.

Spoiler:

It is possible that both CAN see 1, that provides a hint that the total is 3, but it is only a hint.
Neither knows what the other can see, nor can they pass the information between them.

(West: I can see 1, now my esteemed friend can either see 0 [therefore there is only 1], or he can see 2 [thus 3 in total] - now - how can I tell him what I can see ...... and get us out of this predicament)

(East: I can see 1 town .... mmmmm that means there are 3 towns in total, or only 1....I wonder what my esteemed friend can see......)

Spoiler:

I know, that's why I said the answer is either 1 or 3. It is not possible for both of them to see one town, because then the answer would be 2.
If one sees 0, he doesn't know what the other sees, so he waits.
If he sees 1, he waits. The other should see either 0 or 2 (never 1). If the other saw 2, they'd be free on the first day. If they aren't , then he must see 0, so they'll be free on the second day, saying it's 1 town only.
If he sees 2, or 3, he obviously knows the answer is 3 straight away.