[Sparrow]

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:

(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)

If you're partner sees 2 that eliminates 1 as a possible answer - he's only left with 3.