# problem of geometric enumeration

I have the following problem:

Two parallel lines are drawn along a first direction, then three straight lines parallel in a second direction (different from the first direction), and then four parallel straight lines in a third direction (different from the two previous directions). At this stage, a total of 9 straight lines have been drawn and 27 parallelograms drawn in the figure are observed. The construction of the figure is then continued using the same method.

How many lines should one draw at a minimum so that the number of drawn parallelograms is multiple of one million?

Can you help me to find the solution?

• Wouldn't this depend on the exact directions and spacings of the parallel lines? Oct 2 '17 at 12:37
• I think we take the configuration giving the most parallelograms Oct 2 '17 at 12:45
• Then that should be explicitly stated in the body of your question. And even then it's not clear to me that you get a unique answer. Oct 2 '17 at 12:47
• The problem ensures there is a unique answer. Oct 2 '17 at 13:07