Consider a standard 8 by 8 chess board. Black has 4 pieces; a Queen and 3 pawns, which can be placed anywhere on the board. Each pawn is "connected" to the Queen by a straight line.
White has a single piece, the King, which follows standard chess movement rules and begins at square A1 (the bottom left corner of the board).
In this game, black only places their pieces on the grid and does not move. It is white's goal to reach the win condition in as little moves as possible, which is either capturing any of black's pieces, or by landing on a square which contains the straight lines which connect black's pawns to their Queen.
THE PROBLEM: White cannot see black's pieces, but will know when the win condition is met. Devise a strategy for white to minimise the amount of moves taken to reach the win condition for an arbitrary black-piece layout.
Notes:
- I have set this problem myself so if there are any caveats that are not explicit, please let me know and I shall clarify.
- The connecting lines can overlap; 3 or more pieces could be all in a line.
- If a straight line touches the corner of a square, white does indeed win by landing in any of the 4 squares which share that corner.
Example:
[White wins in 3 moves]
Extension: Can the strategy be altered to solve for an n by n, n by m, or arbitrarily shaped topologically connected space?