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 does Team 4 pass through Station E in a day? [This Question was asked as TITA]

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

Answer 1

The Correct Option is A

The objective is to ascertain the number of instances Team 4 traverses Station E, subject to the specified constraints.

Step 1: Fact and Constraint Analysis:

1. Provided Facts:
   • Teams commence at A at 09:00 hrs and must return by 12:00 hrs.
   • At 10:00 hrs, Team 2 is at Station E and Team 3 is at Station D.
   • At 10:30 hrs, Teams 1 and 3 are at Station E.
   • At 11:30 hrs, Teams 1 and 4 are at Stations B and E respectively.
   • Teams 1 and 4 are exclusively on the route between A and E.
   • Team 4 avoids Stations B, D, and F.
2. Constraint 6 (avoidance of Stations B, D, or F) restricts Team 4's possible routes.

Step 2: Deductions from Facts:

1. All teams initiate from A and must complete their routes within a 3-hour timeframe, equivalent to 6 segments of 30 minutes each.
2. Given that Station E is the sole intermediate point and B, D, and F are excluded, Team 4's itinerary must include Station E.
3. At 11:30 hrs, Team 4's location is E. As Team 4 starts and finishes at A, it must have visited E both on its outward and return journeys.

Step 3: Calculation of Team 4's Station E Encounters:

• Trip from A to E: 1 instance.
• Return trip from E to A: 1 additional instance.

Considering Team 4's mandatory return to A by 12:00 hrs and its patrol activity between A and E, it passes through Station E a total of 2 times: once en route to E, and once on the return to A.

The final count is 2 times.