Aspire Faculty ID #16482 · Topic: NIMCET 2009 · Just now
NIMCET 2009

Twelve villages in a district are divided into 3 zones with 4 villages per zone. The telephone department intends to connect villages so 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?

Solution

Within each zone:
Number of pairs among 4 villages = 6 pairs
Each pair has 3 lines → 6 × 3 = 18 lines per zone
3 zones → 18 × 3 = 54 lines

Between zones:
Each zone has 4 villages, so between any two zones: 4×4 = 16 pairs
Each pair has 2 lines → 16×2 = 32 lines per zone-pair
There are 3 zone-pairs → 32×3 = 96 lines

Total lines = 54 + 96 = 150

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