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Classic Diplomacy - Puzzles: Part I, "Trading places"
From the rules:
Units can’t trade places without the use of a convoy.
Two units can exchange places if either or both are convoyed.

1: For how many pairs of provinces is it possible for armies in both of those to exchange places when only one of them is convoyed?
E.g., ALB and TRI, using ADR to convoy one of them while the other moves directly.

2: For how many pairs of provinces is it possible for armies in both of those to exchange places when both of them are convoyed?
E.g., ALB and APU using ADR to convoy one, and ION to convoy the other.

3: How many pairs of provinces are in the answers to both 1 and 2?
E.g., CLY and LVP can trade places when only one of them is convoyed via NAO, and can trade places when both are convoyed, one via NAO, the other via NWG-NTH-ENG-IRI.

3. EDI-CLY, CLY-LVP, LVP-WAL, WAL-LON, EDI-LVP, KIE-DEN, DEN-SWE (7 total)

Provinces need to be adjacent on land and both touch two bodies of water. Furthermore if they share a body of water, there must be a water route between the two bodies of water they don't share that doesn't go through the shared region. Everywhere else on the map with two adjacent two-water provinces, one of the bodies of water is a dead-end, as far as I can tell. For example with NAP-APU the there's no way to convoy using the adriatic but not ionian.

First two questions: more than I want to count!

1. 43, basically all pairs sharing a coastline
2.
Con- Bul
SMY-GRE
ALB-Apu
Tun- any of Nap,Tus,Spa
Spa -any of Naf, Tus
any of Cly, Edi, Lvi, Wal, Lon - any of Cly, Edi, Lvi, Wal, Lon
any of Cly, Edi, Lvi, Wal, Lon - any of Bre, Bel, Nwy
Den - any of Kie, Hol, Swe, Nwy
Kie to Swe
Makes it 53, I think
3. 4 pairs in England, Con-Bul, Kie-Den, Den-Swe, so that makes it 7

I miscalculated, for the 2 question the answer is 48, I forgot that pairs Cly -Cly and the similar ones don't count

Also I forgot about Edi to LVP in 1 and 3 questions, thanks to Liopoli!

liopoil, RZQuasar, wow, that was stunningly quick, and you got really close!

#3: together you folks got all 8 (RZQuasar nicely spotted the eighth, Con-Bul)

#2: RZQuasar, I think you still overcounted just from your concise list, but even so you maybe missed a few, e.g., Bel-Bre via Eng or via Nth-Nwg-Nao-Mao.

#1: I like you reasoning, but it misses a few where the provinces do not share a coastline yet there is a convoy path between them, e.g., Apu-Rom, which share a LAND border but not a coastline, and a convoy using ION and TYS links them.)

THANK YOU BOTH for responding, I am encouraged to work on Part II