Count how many....???
Twelve villages in a district are divided into 3 zones with 4 villages per zone. The telephone department of the district intends to connect the villages with telephone lines such that every two villages in the same zone are connected with three direct lines and every two villages belonging to different zones are connected with two direct lines. How many direct lines are required?
The answer is 150.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Any given village is connected by 3 direct lines to 3 other villages and 2 direct lines to 8 other villages, and is thus connected to 3 ∗ 3 + 2 ∗ 8 = 2 5 direct lines.
There are thus 1 2 ∗ 2 5 = 3 0 0 direct lines emanating from the 1 2 villages in total, but since each of these direct lines is connected to precisely 2 villages there will be 2 3 0 0 = 1 5 0 distinct lines required.