Three minimalist tasks
We will continue the tradition of jointly solving interesting tasks.
Three presented tasks are united by one feature: they contain a minimum of initial data (such tasks are sometimes called qualitative).
Task 1.
An absolutely smooth ball was placed on the edge of an absolutely smooth and absolutely flat horizontal table. No friction, no air resistance. Determine whether the ball will move, and if so, how.
Task 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 everywhere from the Earth. Can a mouse creep into the gap?
Task 3.
One pirate was aware that in an area where the treasure was buried, only three trees grow: oak, pine and birch. In addition, the pirate was known how to find this treasure. First of all, one must stand under a birch facing a straight line connecting the oak and the 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 walk as many steps as you have passed from birch to oak. At this point, you need to drive a peg into the ground (point K 1 ). Then you need to go back to the birch and go from it to the pine, again counting the steps. Reaching the pine, you need to turn at a right angle to the left and walk as many steps as was completed from birch to pine. At this point, you need to drive into the ground a second peg (point K 2 ). The treasure is buried in the middle between the pegs (point K).
The pirate was sure that he would easily find a treasure based on such detailed instructions. But when he came to this area, he found only oak and pine there. Birch disappeared without a trace. However, the pirate still found a treasure. How did he do it?
')
Waiting for your discussions in the comments.
Good luck!
Three presented tasks are united by one feature: they contain a minimum of initial data (such tasks are sometimes called qualitative).
Task 1.
An absolutely smooth ball was placed on the edge of an absolutely smooth and absolutely flat horizontal table. No friction, no air resistance. Determine whether the ball will move, and if so, how.
Task 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 everywhere from the Earth. Can a mouse creep into the gap?
Task 3.
One pirate was aware that in an area where the treasure was buried, only three trees grow: oak, pine and birch. In addition, the pirate was known how to find this treasure. First of all, one must stand under a birch facing a straight line connecting the oak and the 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 walk as many steps as you have passed from birch to oak. At this point, you need to drive a peg into the ground (point K 1 ). Then you need to go back to the birch and go from it to the pine, again counting the steps. Reaching the pine, you need to turn at a right angle to the left and walk as many steps as was completed from birch to pine. At this point, you need to drive into the ground a second peg (point K 2 ). The treasure is buried in the middle between the pegs (point K).
The pirate was sure that he would easily find a treasure based on such detailed instructions. But when he came to this area, he found only oak and pine there. Birch disappeared without a trace. However, the pirate still found a treasure. How did he do it?
')
Waiting for your discussions in the comments.
Good luck!
Source: https://habr.com/ru/post/120850/
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