Question

A, B, C, D, E, and F are the six police stations in an area, which are connected by streets as shown below. Four teams - Team 1, Team 2, Team 3 and 
Team 4 patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.

The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time. 
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs. 
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs. 
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs. 
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E. 
6. Team 4 never passes through Stations B, D or F.
How many times do the teams pass through Station B in a day? [This Question was asked as TITA]

• A. 3 times
• B. 5 times
• C. 4 times
• D. 2 times

Answer 1

The Correct Option is D

To solve this problem, we need to track the movement of the teams and ensure no team repeats a street or disobeys the given conditions. We'll determine how many times the teams pass through Station B. Here is the logical solution:

1. Teams start at Station A at 09:00 hrs and return by 12:00 hrs, given 3 hours for each team to operate.
2. Each street crossing takes 30 minutes, so each team has 6 street moves (back and forth).
3. Teams at 10:00 hrs:
   • Team 2 is at Station E.
   • Team 3 is at Station D.
4. Teams at 10:30 hrs:
   • Teams 1 and 3 are at Station E.
5. Teams at 11:30 hrs:
   • Team 1 is at Station B.
   • Team 4 is at Station E.
6. Team 1 and 4 patrol: Only they patrol the street connecting Stations A and E.
7. Team 4 never goes through Stations B, D, or F, meaning it uses the A-C-E or A-E path.
8. Analyze passage through Station B:
   • Based on the constraints and knowing when each team is at E or not at B determines the route paths.
   • Team 1 goes A-B-C-A to be at B at 11:30 hrs (once passing B).
   • Team 2 could go through B using B-D (once passing B).
9. Now compute passages at Station B, summing the moves:

Team 1 and Team 2 pass Station B once respectively. Combined, they pass twice in total.

Team	Path	Passages at B
Team 1	A-B-C-E-B-A	Once
Team 2	A-C-B-D-C-A	Once

Thus, the teams pass through Station B a total of 2 times in a day.