9
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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.
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  • $\begingroup$ When you push a box, can you push multiple at once? $\endgroup$ – Deusovi Dec 12 '17 at 2:41
  • $\begingroup$ @Deusovi Yes, that is correct. As long as there's an empty cell at the end of the line of boxes you're pushing. $\endgroup$ – Riley Dec 12 '17 at 2:41
  • $\begingroup$ Are these the same conditions as this puzzle?: puzzling.stackexchange.com/questions/55853/… $\endgroup$ – D Krueger Dec 12 '17 at 2:42
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    $\begingroup$ @DKrueger Close, but that puzzle did not allow you to move the objects. This one does. $\endgroup$ – Apep Dec 12 '17 at 2:43
  • $\begingroup$ @DKrueger Actually, I was inspired by that question, but this one's completely different in the mechanics and the objective. $\endgroup$ – Riley Dec 12 '17 at 2:44
9
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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

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  • $\begingroup$ 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. $\endgroup$ – Riley Dec 12 '17 at 17:16
3
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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.

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  • $\begingroup$ How do you get to the top right, bottom left, or bottom right corners? $\endgroup$ – Riley Dec 12 '17 at 3:17
  • $\begingroup$ I think you misinterpreted the question. You must be able to occupy every cell. Not just touch every box. $\endgroup$ – Riley Dec 12 '17 at 3:21
  • $\begingroup$ I tried again... $\endgroup$ – R.M Dec 12 '17 at 3:36
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    $\begingroup$ Your answer's great, but it's not optimal. $\endgroup$ – Riley Dec 12 '17 at 3:39
  • $\begingroup$ Ok. Working on it! :) $\endgroup$ – R.M Dec 12 '17 at 3:43

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