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 address this problem, we will monitor team movements, ensuring no street repetition or condition violations. The objective is to count the number of times teams traverse Station B. The logical solution is as follows:

1. Each team operates for 3 hours, commencing at Station A at 09:00 hrs and concluding by 12:00 hrs.
2. Each street crossing takes 30 minutes, allowing for 6 street movements (outbound and return) per team.
3. Team positions at 10:00 hrs:
   • Team 2 is located at Station E.
   • Team 3 is located at Station D.
4. Team positions at 10:30 hrs:
   • Teams 1 and 3 are both at Station E.
5. Team positions at 11:30 hrs:
   • Team 1 is at Station B.
   • Team 4 is at Station E.
6. Team 1 and 4 patrol route: Their patrol is restricted to the street connecting Stations A and E exclusively.
7. Team 4's movement constraints: It does not pass through Stations B, D, or F, indicating its path is limited to A-C-E or A-E.
8. Analysis of passages through Station B:
   • Route paths are deduced from the constraints and known team locations at E, and whether they are not at B.
   • Team 1 reaches Station B at 11:30 hrs via the path A-B-C-A, having passed B once.
   • Team 2 could have passed through Station B by taking the route B-D, resulting in one passage through B.
9. Now, calculate the total passages at Station B by summing individual moves:

Team 1 and Team 2 each pass Station B once. In total, they account for two passages.

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

Consequently, the teams collectively pass through Station B a total of 2 times within the operational day.