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I assume the "three block conveyor path" that you are thinking about is the up, right, down conveyor path in the upper left corner of the raised section with the movement blocks. I assume this because:

1. The bottom corners are out because if you were able to move the left arrow down without a conveyor path, then the conveyor path would not be necessary.
2. If you were to try to make a three block conveyor path in the upper right corner, then you would need to use the left movement block in it, making it impossible to use that conveyor path to make it go down as there is only one leftward movement block available.

This is how it looks before I put the left movement block in the three block conveyor path (made up of up, right, then down movement blocks):

This is how it looks after putting the block in the three block conveyor:

This happens because when blocks, or bombs are put in the conveyor belts, then the character is unable to move. This means that the block goes up, right, then down and hits the character, forcing the character to be always either to the right of the block or below the block. This shows that it is impossible to do it that way to make the block go down.