no of parallelograms??

umaa · Posted: Tue Jul 08, 2008 9:29 pm Post subject: no of parallelograms??

The number of parallelograms that can be formed from a set of FOUR parallel straight line intersecting a set of THREE parallel straight lines=?

Options are,

a. 9
b. 12
c. 6
d. 18

amitdgr · Posted: Wed Jul 09, 2008 1:36 am Post subject: Re: no of parallelograms??

umaa · Posted: Wed Jul 09, 2008 1:48 am Post subject:

No my friend. I've got the same answer. The answer is 18 (d).

amitdgr · Posted: Wed Jul 09, 2008 2:16 am Post subject:

Ian Stewart · Posted: Wed Jul 09, 2008 4:43 am Post subject:

You're only counting the six smallest parallelograms in the picture (nice picture, by the way!). If, for example, you take all six of the small parallelograms and consider it to be one shape, you get one large parallelogram. And there are many others:

6 parallelograms that measure 1 across, 1 vertical (smallest possible)
3 parallelograms that are 2 across and 1 vertical
4 parallelograms that are 1 across and 2 vertical
2 parallelograms that are 2 across and 2 vertical
2 parallelograms that are 1 across and 3 vertical
1 parallelogram that is 2 across and 3 vertical (all of them together)

Hope the terminology makes sense. That's a total of 18 parallelograms.

umaa · Posted: Wed Jul 09, 2008 5:02 am Post subject: Thanks

Thanks Ian. I missed that out. Laughing

amitdgr · Posted: Wed Jul 09, 2008 5:05 am Post subject:

cubicle_bound_misfit · Posted: Wed Jul 09, 2008 10:18 pm Post subject:

you need to choose 2 parallel lines along with 2 vertical line.

2 parallel lines can be chosen from 4 parallel line in 4C2 ways .
2 vertical lines can be chosen from 3 vertical line in 3C2 ways

together the condition can be chosen in 4C2 * 3C2 ways ==18.

Hope that helps.

Regards,