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While I was watching Phi-Brain Episode 2, I tried solving the puzzles on my
own. But on that sliding block game, I couldn't figure out how Gammon solved
that puzzle **without moving the red car until the path was cleared**. Here's
how it looks like:  
  
![enter image description here](https://i.stack.imgur.com/tVp1f.png)

The black car on the farthest left and the white car near the exit are 3
blocks long which can be confirmed from this picture below.  
  
![enter image description here](https://i.stack.imgur.com/HIblP.png)

So when you plot it out, the puzzle would look like this:  
  
![enter image description here](https://i.stack.imgur.com/9bCpp.png)

I'm kinda wondering how and I don't think it's possible.


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2015-04-29T02:56:36.037
21221
2016-10-21T14:00:30.843
2015-04-29T03:47:22.537
question
phi-brain
How did Gammon solve the puzzle in episode 2?


I ended up writing a descriptive model for it in
[IDP](https://dtai.cs.kuleuven.be/software/idp), letting the solvability
prover from our univeristy prove whether a solution can be found. The fastest
solution it could come up with was one finishing the game in **48 steps** (see
below). Therefore the problem is indeed solvable. My first answer though,
saying Gammon cheated, was indeed incorrect. It was only **after** he had
solved the puzzle, that the system was sabotaged and made Kaito _cheat_ to
save their lives.

I numbered the cars from top to bottom and left to right as in the following
picture.

![enter image description here](https://i.stack.imgur.com/1Kgdtm.jpg)

The solution is written in the form `Move(t,cid,d)` with `t` being the step
number in the solution, `cid` being the car identifier and `d` being the
distance the car travels during that time step. `d` is positive when driving
up or to the right and `d` is negative when driving down or to the left.

[code]

    Move = {
        1,9,1; 2,4,2; 3,2,1; 4,1,-1; 5,6,-3;
        6,7,1; 7,9,1; 8,3,3; 9,7,-2; 10,6,1;
        11,1,1; 12,2,-1; 13,5,3; 14,2,1; 15,1,-1;
        16,6,-1; 17,7,2; 18,8,2; 19,10,-4; 20,8,-2;
        21,7,-1; 22,6,1; 23,1,1; 24,2,-1; 25,5,-3;
        26,2,2; 27,1,-1; 28,6,-1; 29,7,1; 30,3,-3;
        31,7,-1; 32,6,1; 33,1,1; 34,2,-2; 35,4,-2;
        36,9,-4; 37,4,2; 38,2,1; 39,1,-1; 40,6,-1;
        41,7,1; 42,3,3; 43,7,-1; 44,6,3; 45,1,1;
        46,2,-1; 47,5,4;
    }
    
[/code]


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2015-04-29T08:11:18.723
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2015-10-05T01:03:47.820
2015-10-05T01:03:47.820
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answer