Work backwards from the target
A sliding puzzle is not a search for a good move. It is a short list of things that have to happen, and the list is written backwards.
Start at the target. Name every block standing in its lane. Those are the blockers, and each one has to leave the lane.
Now take one blocker and ask the same question about it. What is in its way? That answer is the next name on the list. Keep going until you reach a block that can move right now. Move that one first.
Two blockers often wait on the same block. That block is the one to move, because moving it frees both.
On the tile boards the same idea has a shape. Finish the top row, then the left column, and leave them alone. Each one you finish makes the board smaller. What is left at the end is a 2 by 2 corner, and that corner is a short shuffle.
Six vehicles, five moves
The red car is in row 3. Three vehicles stand in that row: the lorry in column 4, and the two cars in columns 5 and 6.
The lorry can drop straight down, because the three cells under it are empty. That is one blocker gone.
Of the two cars facing down the board, only the one in column 6 can move now, and it can go down. The car in column 5 cannot move at all. The car lying across row 1 is on top of it, and a lorry is under it. So the car across the top is the block it waits on. Move it left.
Now the car in column 5 goes up into the space that car left, and the car in column 6 goes down. Row 3 is empty, and the red car drives out.
The five moves are: lorry down three, car across left two, car up one, car down two, red car right and out.
Which car moves next?
Here is the same lot two moves in. The lorry has dropped and the car across the top has moved left.
Two cars are still in row 3, and both have to leave it. A lorry fills the three cells under the car in column 5. The car in column 6 has the rest of its column to itself.
Try it
One of those two cars has only one way to go. Which one?
- The car with the lorry under it
- The car in the last column
Show the answer
The car with the lorry under it
Correct. The lorry fills the cells under that car, so its only way is up, into the space the top car left.
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