The tilted labyrinth - Can you find the fastest path in this 3D-puzzle? (Simulator now included.)

Question

This is a puzzle was inspired by the board game labyrinth, which I very much enjoyed as a kid.

It either requires very good 3D-visualization skills in your brain or some paper & scissors work. (Hence mechanical puzzle).

Thanks to Kevin, there is now also a Javascript simulator for this puzzle, which makes things way easier.

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Goal

Imagine you have a labelled board of 25 fields like the following:

You also have 25 dice which are all build up by the same mesh:

These dice are placed on a 5x5 field grid to create a labyrinth with the faces showing upwards.

You start out on the top-left position (A1), and you goal is to reach all other three corners (E1, E5, A5 ) in arbitrary sequence. You want to do this with minimum amount of steps. Note that 'passing through' one of the corners in a single move is valid for the purpose of the goal. (You do not have to end a move in a corner. )

Rules

• A single step consists of the sequence of first tilting a row or column and then moving from your current location along 'open paths' for an arbitrary distance. (You may do only one of the two, but not change the sequence order.)

• When tilting, you have to tilt all dice of the row/column in the same direction by 90 degree. (Fixed tiles of the row/column stay obviously unchanged.)

• You must not tilt a row/column which includes your current position on the grid.

• the board does not warp around. It is not possible to leave it on one side and renter from the other side.

Notation

• Tilt-notation includes either the letter (column) or the number (row) of the tilt, and either + or - to indicated direction (see example below).

• Move-notation includes start and end position given by the grid-coordinates (see example below).

Example

Starting from the start position given above, you first all dice of column B in + direction. (Imagine the top of the dice tilting downwards.)

Tilt-Notation: (B+)

Now you move the marker.

Move-Notation: [A1 -> B1]

So the whole step would have the notation:

Step 1: (B+) [A1 -> B1]

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The puzzle question:

What is the minimum number of steps you need to visit all 4 corners of the grid (starting in A1) from the given starting situation:

You have to give all steps in the notation explained above.

The current record for this puzzle is 7 moves.

Answer 1

Here's a 7-move answer.

(B+),
(C+),
(D-),
(D-),
(2+), [A1 -> E1],
(B-), [E1 -> A5],
(D-), [A5 -> E5]

Also, obviously, done with help from Kevin's tool.

Answer 2

NEW ANSWER: 10 Turns (I used Kevin's interactive tool for this one)

(2-)
(2-)
(3+)
(4+)
(4+)
(C+), [A1 -> C5]
(4-)
(3-)
(2+), [C5 -> E1]
(3+) [E1 -> E5]

OLD ANSWER: 13 turns

Just to get the ball rolling my moves are as follows (I created an interactive version in Excel, so there is plenty of margin for error.):

(B+)
(C+)
(D+)
(E+)
(E+) [A1->E1]
(2-)
(3+)
(4+)
(5-) [E1->E5]
(4-)
(B+)
(B+)
(A+) [E5->A5]