Saturday, January 26, 2008

No retrace and 3 D to 2 D without bridge

Two more puzzles.

I will give you a set of points on a plane and also define the connectivity of all points which are connected with straight lines. There will be certain figures which can not be drawn without lifting the pen or without retracing the path. For example – You can not draw A without lifting the pen or without retracing any part of any line. You have to device a simple algorithm check which should tell this about any complicated figure.

What will the algorithm be?

Hint: While thinking about the solution – think about the counter examples.

Imagine a cube made of wires. This can be represented on a 2-D as given in the figure which follows.

I bridge is defined as in the figure which follows next.

If I connect two opposite points of the cube with a wire, will it be possible to draw that structure on 2D without using a bridge?

Hint: Think this problem as a current resistance problem.