Thursday, 6 November 2014

logical deduction - A Special Parking Lot


There is a special kind of parking lot that stores special 1x1 cars that only can move to adjacent squares not including diagonals if they are empty (provided no car occupies the square). Every car occupies exactly one square and no more. The exit is beside the top left corner of the parking lot.


Because everyone is a perfect driver, everyone parks in a way that every car can exit without moving any other cars.




Currently, there are 24 cars parked in a 7 by 7 parking lot of this kind. Can you fit more cars in a different arrangement?




Answer



No idea if this is optimal (also have no proof), but it's possible to do



28



Example:




Parking



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