Question

You have 3 points labelled A, B and C. You then have another 3 points labelled
1, 2 and 3. The aim of the puzzle is to connect point A with point 1, 2 and 3. Point
B with point 1, 2 and 3 and point C with point 1, 2 and 3.

Now while connecting the points you have to follow one rule - the lines cannot
cross over each other.

A B C
1 2 3

Answer 1

There is no solution to it, if you consider 2 dimensions. It is impossible to join
each of points A, B and C with points 1, 2 and 3 without lines crossing each
other.
There is solution, if you consider 3 dimensions. Consider a circular base and a line perpendicular to it passing from the center. Now take any 3 points along the perimeter of the circular base as points 1, 2 and 3. Similarly take any 3 points along the perpendicular line as points A, B and C. Now it is quite simple to join each of points A, B and C with points 1, 2 and 3 without any of the lines crossing each other.
The other possible 3D structure is Pyramid. Take points 1, 2 and 3 as a vertices of the triangular base and points A, B and C along the height of the Pyramid which is perpendicular to the triangular base and passing through the apex.