9

You own a warehouse which is a 7x7 grid of cells. You must arrange a maximal number of boxes in the warehouse so that you are able to travel to any given cell. Here are the specific conditions:

  • You start at the top left cell.
  • You may not occupy the same cell as a box, and all boxes must be in distinct cells.
  • You are allowed to move to an adjacent cell if it's free, or if you can push the box(es) in your way.
  • You are not required to visit every cell. You are simply required to be able to visit any given cell from the initial configuration.
Riley
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2 Answers2

9

Here's a solution for

29 boxes.
Red cells represent boxes. Denote topmost row as row 1
boxes

Solution for accessing bottom 5 rows is trivial:

Push boxes in the same row as target cell toward the two top corners. For example, to access row 3:
more boxes

Solution for accessing row 2:

Same as above really. Diagram below shows how to access the left half of row 2; horizontally mirror to access right half. Note that this grants you access to the middle cell of Row 1.
yet more boxes

Solution for accessing remainder of row 1:

Simply start in one of the top corners, and push horizontally :) Sample solution for accessing left half of Row 1:
box box box box

kwypston
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  • Good job! 29 is the best I've personally been able to come up with. If no one can do better in the next few days or so, I'll accept your answer. – Riley Dec 12 '17 at 17:16
3

28 boxes:

enter image description here

.

Obviously, you can get to the outer two rows.

.

To get to the 9 spaces in the center, push boxes from top or bottom (Whichever is closest), then get the extruded boxes out of the way on the opposite side, then repeat. enter image description here

Sorry for all the confusion. This is my last answer.

Edit: added explanation.

Reinis Mazeiks
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