Posts from Quiz Auto-translated

Ah, so that's how it is, even in 3 turns: 5 - to the left 4 - upwards 5 - diagonally downwards Done

You can’t move diagonally.

Hmm, well, it's probably my fault that I didn't specify this earlier. But yes, it only moves horizontally and vertically.

Shall we part ways, guys? (of course not)

Of course.

Excellent article, now I can indulge in mindless activities with a clear conscience.

18 turns. Or 17. Something like that. Basically, first, rotate the entire caterpillar to the left so that 5 is at the bottom, then don't touch the last column and rotate the remaining 4 (1, 2, 3, 4) to the left. Then move 4 from the top to 5. Done.

Excellent article, now I can degrade with a clear conscience.

Trying to "become smarter" at 20+ is like trying to learn how to fly.

18 moves. Or 17. Something like that.

Basically, first, rotate the entire caterpillar to the left so that 5 is at the bottom, then don't touch the last column and rotate the remaining 4 (1, 2, 3, 4) to the left. Then move 4 from the top to 5.

Done.

It seems plausible, but could you describe the solution in more detail so I can be sure? Also, please state the exact number of moves.
For brevity, just write the number you're moving at each step, without specifying the direction, because the direction can always only be one (towards the empty cell).
Of course, I'd also like to know why it can't be done faster, but as promised, I won't demand it.

You can create a graph where each vertex corresponds to a specific arrangement of the tiles. :) There will be a total of 6*5! = 720 vertices. Connect the vertices with edges representing possible transitions from one state of the board to another, and calculate the shortest paths from the state shown in the image to all possible states where the tile '4' is above the tile '5' in the rightmost row. :D The shortest of these paths will be the answer.

You've learned a lot, my friend. However, I'd be happy to watch. :D

Yeah, I'm already confused. Never mind, I don't know.

But generally speaking, is it solvable?

Added 4 minutes later
I don't think so.

Honestly, I'm already confused. Never mind, I don't know.

But generally speaking, is it solvable?

(
Yes, it's solvable.

I don't think so.

If you're sure about that, you can try to prove it...

Trivially, we rotate the first 4 cells. The numbers 5 and 4 swap places and end up in the adjacent column. We rotate again. The numbers swap places again and end up in the adjacent column. But there are only 3 columns, so no matter how many times they swap places, they won't end up swapping places in the original column. Also, if you simply move them in a snake-like pattern, the same result is obtained.