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You are playing a game on the following 4x4 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?

enter image description here

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3 Answers 3

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Is this a trick question? (New here)

Is the answer just

"yes"?

Otherwise,

up left up right

up right up right

down right down left

up right down

The trick is to "disrupt" the alignment of two balls that the instinctive approach wants to line up against the right wall.

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    $\begingroup$ Correct and well done! $\endgroup$
    – Dmitry Kamenetsky
    Mar 15, 2022 at 9:52
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    $\begingroup$ Yay! Thanks @DmitryKamenetsky $\endgroup$
    – user
    Mar 15, 2022 at 13:20
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@user already posted a solution, mine differs slightly at the end:

ULU RURUR DR ULURD

(spaces inserted at the points where I was mentally switching to another task; the final 5 moves are where the solution differs from @user's)

This is what it looks like:

enter image description here

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    $\begingroup$ Thank you for the animation. $\endgroup$
    – Dmitry Kamenetsky
    Mar 15, 2022 at 9:53
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I have a completely different solution, the same length as the other two at time of posting - still 15 moves. I am wondering if there is a way to solve this in less than 15 moves.

URURD LUR DRD LURD

After the first five moves, the grid looks like this:

URURD (one of the orange balls has not moved as no left move has been made): enter image description here

After the next three, it looks like this:

LUR: enter image description here

After the next three:

DRD: enter image description here

And the final four moves complete it:

LURD: enter image description here

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    $\begingroup$ As far as I can tell, the position shown in your second spoiler block is unavoidable, and there are two ways to reach it in 8 moves, and then two ways to reach the goal from there in 7. (The final 7 moves in @user's solution match yours.) So we may expect one more answer with a different path of 15 moves, using your beginning and my finish :-) $\endgroup$
    – Bass
    Mar 15, 2022 at 18:12
  • $\begingroup$ Nice work. I can confirm that 15 moves is optimal. $\endgroup$
    – Dmitry Kamenetsky
    Mar 16, 2022 at 0:05

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