Sliding balls on a 5x5 grid

Question

You are playing a game on the following 5x5 grid. Each turn you can slide all the orange balls into one of four directions: left, up, right or down. A ball will continue sliding along a direction until it hits a wall (solid blue squares), boundary of the grid or another ball. All the balls move at once. Walls do not move. Can you get the balls to finish on the target (T) cells?

Answer 1

This is definitely a bit more difficult that the ones before, but despite OP's warnings in the comment section, there's no need for any kind of brute force. (There's an answer with a solution already, but it doesn't explain how to actually find the solution.)

Here's how to get there by retrograde analysis:

• The T at r2c2 tells us the final move must be "up".
• The T on row 1 tells us the move before cannot have been "right". Since having "up" or "down" before an "up" doesn't change anything, the penultimate move is "left".
• This means the ball that ends up at r2c2 can only have come from r4c2, which means it was in the corridor at the bottom right before that
• There's a T in that corridor, so there were two balls in there
• To get a ball into the corridor on the bottom right, there must be another ball at r5c2.

With these in the forward order, we have the following goals:

1. bring a ball to the lower left corner
2. use that ball as a stepping stone to get the other balls to the corridor at the bottom right
3. bring the stepping stone ball back to the upper right corner
4. everything will now line up perfectly for the final "left-up".

But there's a problem: if we try to use one ball as the stepping stone, and bring the other balls one-by-one, we can't just "bring the third ball": either the stepping stone ball or the one ball already in the corridor will escape. So we need to do a sneaky juggle to bring all the balls to the bottom left, which finally solves all our problems. Like so:

I didn't notice any alternative paths along the way, so this is very likely the exact same answer @noedne posted. (After double checking, it indeed is.)

Answer 2

LDRD LDRD RD LULD LDRD RDR U LDRD R URU LU

The complete solution can be found by continuously finding the only way to make progress, i.e., moving the balls into a previously unvisited state. Here is a detailed explanation of all of these progress steps:

LDRD: Move ball 1 to the bottom left.
LDRD: Move ball 2 to the bottom left.
RD: Move ball 2 to the bottom right.
LULD: Move ball 3 out while moving ball 2 back to the bottom left.
LDRD: Move ball 3 to the bottom left.
RDR: Move ball 3 to the bottom right.
U: Move ball 2 out.
LDRD: Move ball 2 to the bottom left.
R: Move ball 2 to the bottom right.
URU: Move ball 1 to the top right.
LU: Move ball 2 to the top left.