How did Gammon solve the puzzle in episode 2? 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:


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.


So when you plot it out, the puzzle would look like this: 


I'm kinda wondering how and I don't think it's possible.
I ended up writing a descriptive model for it in 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.



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.

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;
}