Amazing Questions Without Answer Problem 12.3: Three unfriendly neighbors use the same water, oil and treacle wells. In order to avoid
meeting, they wish to build non-crossing paths from each of their houses to each of the three wells. Can this be done? 
We know that the answer of this question is No, since the bipartite graph $k_{3,3}$ is not a planar graph. 
My Question: Are there some questions such as Problem 12.3 that ask to do or draw something but mathematically is not possible. 
I would appreciate to suggest questions with math level similar to Problem 12.3.
Please edit my question for suitable tags. Thanks
 A: After your comment, I want to add something but it will be too long for a comment.
In graph theory, not all the questions are stated in this way (like giving an example from real life) but questions that ask "Prove that the following graph is non-planar" are all the same kind and although it is not possible, we can prove that it is impossible to draw those graphs planarly (For example see non-planarity of Petersen Graph using Kuratowski's theorem).
As given in the duplicate, there are also some questions that ask whether "Euler Path" exists or not as in the problem Seven Bridges of Königsberg, which can be proven that such path doesn't exist.
However these questions are different from the questions that have "no answer". In mathematics, generally proving impossibility of a statement is as valuable or important as proving that statement holds. Because question asks "Can this be done?" and answer is simply "No" and it can be proven when this is the case.
However in an example like Travelling Salesman Problem, the question "Can it be done with a certain complexity" is an open question and has no known answer (Notice that it is a matter of complexity so we know that it can be solved in some complexity but we don't know whether there exists an algorithm that solves it more efficiently).
