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You are given a 4x4 grid with 3 crosses as shown below. Each turn, you can select a cross and slide it along horizontally or vertically. It will continue sliding until it hits another cross or a wall. Can you get a cross into one of the squares in the central 2x2 subgrid? Bonus: can you get multiple crosses into the central 2x2 subgrid?

enter image description here

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4 Answers 4

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Is one cross possible?

Yes

Multiple crosses?

Also Yes

Note that the sequence for the first cross is essentially the same as the 3x3 version.
enter image description here

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    $\begingroup$ 25 seconds between our answers! :P Think they are practically the same just different orientation, nice stuff! $\endgroup$ Oct 19, 2023 at 13:10
  • $\begingroup$ Correct and well done! I think this answer came slightly earlier and also uses fewer moves. $\endgroup$ Oct 19, 2023 at 13:16
  • $\begingroup$ You can now try this one puzzling.stackexchange.com/questions/122811/… $\endgroup$ Oct 19, 2023 at 13:23
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It is, in fact,

possible.

As shown here:

XX..
X...
....
....
XX..
....
....
X...
XX..
....
....
...X
.X..
....
....
X..X
.X..
....
....
XX..
....
....
.X..
XX..

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For the bonus, you can actually

Get 2 in the middle:

By doing the following:

enter image description here

Where blue shows the old position of the X, and green the new position

Note from this position it is clearly impossible to get the third in the middle, as it can only slide around the corners

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The path to get two in the center is now 9 moves long (thanks Daniel Mathias). There are other move sequences producing the same path length.

xx..  xx..  .x..  .x..  .x..  ...x  ....  ....  ....
....  ....  ....  ....  .x..  .x..  .x..  .x..  .x..
....  ....  ....  ....  ....  ....  ....  ....  .x..
x...  ...x  x..x  xx..  x...  x...  x..x  xx..  x...

Now, can you get all three in the center?

Nope, not possible. Reason for that is fairly simple. Start from no pieces in the center and put the first in the center. This means that another piece is on the edge, next to the central piece (or the central piece would not stop in the center). From that place, the edge piece can only move to corners or until it touches the other non-central piece. It cannot move to the center directly, and it cannot stop on the edge without the help of the other piece. So, we can (pretty easily) position the remaining two x side by side anywhere on the edge. However, from that position, only one can stop in the center by hitting the other central piece.

Interestingly,

Giving us 4 x to play with in any starting configuration, it is trivial to put all 4 in the center. Put two in the center next to each other, then put two side by side on the opposite edge (put one in the corner, move the other next to it, slide the corner one over). Then slide both over and we end up with all 4 x in the center. This general recipe in the brackets of two pieces walking along the edge allows for getting 4 x in the center for arbitrary board side.

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    $\begingroup$ The shortest paths require only nine moves. $\endgroup$ Oct 21, 2023 at 3:47

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