Venice Connection 1.0 - Solution
Several entrants noted the Nim-like qualities of the game and submitted solutions that relied on the solution to that game: leave your opponent with 4 pieces. Unfortunately this doesn't work in Venice Connection due to the added property of tile location and the fact that all the tiles you place must be touching each other. For example, consider the following situation:
You've left your opponent with four tiles to place, smugly thinking that you've got the game won. She then smiles coyly and places two tiles thus:
Suddenly you're not so smug.
In any event there were several solutions to last month's puzzle. I'll present the intended solution simply because it's very easy to show that it is indeed a winning move. Place tiles G & H so that you have the following:
Clearly the only way to complete the puzzle is to place appropriate tiles in the locations marked I,J,K,L & i,j,k,l. If your opponent makes any other move you may win by calling "impossible". Since these areas are symmetrical, you can guarantee a win simply by mimicking any subsequent move your opponent makes, replacing I for i, J for j, K for k and L for l as appropriate. (Or vice versa as the case may be.) So if your opponent plays k & j, you respond by playing K & J. Similarly, if your opponent plays L, you respond with l. This guarantees that you will place the last tile and win the game.
There were other solutions quite different from this but they were substantially harder to prove. (For the record, I did not require you to prove your move was a winning one.) In any case, congratulations to Les Willey whose name was drawn from the list of correct entrants.
- Greg Aleknevicus