Three minimalistic challenges

    We continue the tradition of jointly solving interesting tasks.
    The three presented tasks are united by one feature: they contain a minimum of initial data (such tasks are sometimes called qualitative).

    Problem 1.

    An absolutely smooth ball was placed on the edge of an absolutely smooth and absolutely flat horizontal table. There is no friction, no air resistance. Determine whether the ball will move, and if so, how.

    Problem 2.

    Imagine that the globe is tightly wrapped around the equator with a rope. Suppose that the length of this rope was increased by 1 meter and positioned so that it is equally spaced from the earth everywhere. Can a mouse crawl into the resulting gap?

    Task 3.

    One pirate knew that in the area where the treasure was buried, only three trees grow: oak, pine and birch. In addition, the pirate knew how to find this treasure. First of all, you need to stand under a birch facing a straight line connecting the oak and pine. In this case, the oak should be on the right, and the pine on the left. Then you need to go to the oak tree, counting the steps, and when you reach the oak tree, turn at a right angle to the right and go through as many steps as you have already walked from birch to oak. In this place you need to drive a peg into the ground (point K 1 ). Then you need to return to the birch and go from it to the pine, again counting the steps. When you reach the pine tree, you need to turn at a right angle to the left and go through as many steps as were passed from the birch to the pine tree. In this place you need to drive a second peg into the ground (point K 2) The treasure is buried in the middle between the pegs (point K).
    The pirate was sure that he could easily find the treasure according to such detailed instructions. But when he arrived in this area, he found there only oak and pine. The birch disappeared without a trace. However, the pirate still found the treasure. How did he do it?

    Waiting for your discussions in the comments.
    Good luck!

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