2. (8 points) A poplar tree, a willow tree, a locust tree, a birch tree, and a sycamore tree are planted in a row, with a distance of 1 meter between each adjacent pair of trees. The distance between the poplar tree and the willow tree, and the poplar tree and the locust tree is the same. The distance between the birch tree and the poplar tree, and the birch tree and the locust tree is the same. Therefore, the distance between the sycamore tree and the birch tree is
meters.
2
【Solution】Solution: The distance between the poplar tree and the willow tree, as well as the locust tree, is equal, so the possible positions of the three trees could be: Willow $\square$ Poplar $\square$ Locust, Willow Poplar Locust $\square \square, \square$ Willow Poplar Locust $\square, \square \square$ Willow Poplar Locust, where $\square$ represents an unknown position. Since the distance between the birch tree and the poplar tree, as well as the locust tree, is also equal, the only possibility is: Willow $\square$ Poplar Birch Locust, with the remaining position being the plane tree.

Therefore, the distance between the plane tree and the birch tree is 2 meters.
The answer is: 2.