Garden with mushrooms

Question

A farmer cultivates mushrooms in his garden. A greedy neighbor wants to pick some but the farmer is trying to block him.

The garden has the form of a 8x6 grid. Rows 1 to 8 from the front to the back and columns A to F from left to right. The mushrooms are planted in the 8th row (6 mushrooms). The farmer is initially standing at the block E7, right in front of the mushrooms and can move at any of his direct surrounding 8 blocks (including those behind him, where the mushrooms are planted). The neighbor initially stands at block F1 and is trying to reach the mushrooms by walking at any of his directly surrounding blocks (including those situated diagonally in relation to his position). Once the neighbor reaches the farmer, he hits him and can then reach the mushrooms, but if the farmer reaches the neighbor, he hits him also, and he has to back out. The neighbor moves first and then they alternate turns. Will he manage to get at least one mushroom, or the farmer will block him? To summarize, the "game" ends in any of the 3 cases:

1. The farmer reaches the neighbor (walks on his square). In this case, the neighbor has to leave and go home.

2. The neighbor reaches the farmer, even once (walks on his square). Then the farmer has to admit he lost, and let him get the mushrooms!

3. The neighbor reaches one (any) mushroom before the farmer manages to stop him.

Describe some of the optimal moves for each of them, using the grid coordinates.

I tried to set the neighbor "chase" the farmer by trying to be on the same column with him but can't find a general pattern.

FYI I found this in an Ukrainian magazine at the Kiev airport - I hope I translated everything correctly!

Answer 1

The neighbor can win. He starts to E1 and claims the distant opposition. If the farmer moves forward, so does the neighbor. If the farmer moves sideways the neighbor moves diagonally forward on the side away from the farmer. Now the farmer must move toward the neighbor and the neighbor can move in front of the farmer an even number of spaces away, maintaining the opposition. Again the farmer must move sideways one way and the neighbor moves diagonally forward on the other side.

A game might go
E1 D6
F2 E6
E2 D6
F3 E5
E3 D5
F4 E6
E4 D6
F5 and the neighbor can get the F mushroom

Answer 2

It appears that, unless the farmer takes a deliberately bad path, he will always be able to hit the neighbor. Here are sample moves juxtaposed. In the 2nd example, the farmer could have avoided being hit by taking a different path. The neighbor can only be hit or move to places to avoid being hit but he cannot get past the farmer if the farmer moves wisely.

N1: 2F 3E 4D

F1: 6F 5E 4D-HIT

N2: 2E 3D 3C 4C-HIT

F2: 6E 5D 4C

N3: 2E 3D 3C 4D

F3: 6E 5D 5C 4D-HIT