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.

Which one among the following stations is visited the largest number of times?

To find which station is visited the largest number of times, we can trace the routes of the four teams step-by-step. The connections between the stations are shown in the diagram below:

Each team patrols continuously for 3 hours (from 09:00 to 12:00 hrs.), which is exactly 180 minutes. Since crossing any street takes 30 minutes, each team makes exactly 6 street crossings. Let us define the time intervals and checkpoints as:
T₀ = 09:00 (Start at A)
T₁ = 09:30
T₂ = 10:00
T₃ = 10:30
T₄ = 11:00
T₅ = 11:30
T₆ = 12:00 (Return to A)

Step 1: Analyzing Team 4's Route
According to the rules:
- Team 4 never passes through stations B, D, or F (Fact 6).
- The only allowed stations for Team 4 are A, C, and E.
- Looking at the connections, C is only connected to A and D (since D is forbidden, Team 4 can only go A ↔ C).
- Similarly, E is connected to A, D, and F (since D and F are forbidden, Team 4 can only go A ↔ E).
- Therefore, Team 4 must alternate between A and {C, E}. This means Team 4 must be at A at times T₀, T₂, T₄, and T₆, and at C or E at times T₁, T₃, and T₅.
- Fact 4 states that Team 4 is at station E at 11:30 (T₅).
- Fact 3 states that only Teams 1 and 3 are at station E at 10:30 (T₃), which means Team 4 must be at C at T₃.
- At T₁, Team 4 must be at E because if it were at C, it would conflict with Team 3 moving from A to C (as explained below).
Thus, the path of Team 4 is: A → E → A → C → A → E → A.

Step 2: Analyzing Team 3's Route
- At T₂ (10:00), Team 3 is at D (Fact 2). Since it starts at A and cannot use the street A-E (Fact 5), the only path to reach D in 2 steps is A → C → D.
- At T₃ (10:30), Team 3 is at E (Fact 3).
- To return to A by T₆ (12:00) without using the street E-A (which is reserved only for Teams 1 and 4), Team 3 must go back via D and C.
Thus, the path of Team 3 is: A → C → D → E → D → C → A.

Step 3: Analyzing Team 1's Route
- At T₃ (10:30), Team 1 is at E (Fact 3).
- At T₅ (11:30), Team 1 is at B (Fact 4). Since the only neighbor of B is A, Team 1 must be at A at T₄ (11:00) and T₆ (12:00).
- At T₃, Team 1 is at E and needs to reach A at T₄. Since only Teams 1 and 4 can use the street A-E, Team 1 goes E → A.
- Prior to T₃, Team 1 starts at A at T₀, visits B at T₁, and returns to A at T₂.
Thus, the path of Team 1 is: A → B → A → E → A → B → A.

Step 4: Analyzing Team 2's Route
- At T₂ (10:00), Team 2 is at E (Fact 2). Since it cannot use the street A-E, it must take the path A → F → E.
- From E at T₂, it must leave because Teams 1 and 3 are the only ones at E at T₃. It can travel to F, resulting in the path F → E at T₁-T₂ and E → F at T₂-T₃.
- The remaining steps of Team 2 will visit F and/or C, eventually returning to A at T₆.

Step 5: Counting the Visits to Stations (excluding Station A)
Let us sum the number of visits to each station from the paths of Teams 1, 3, and 4:
- Station B: Visited 2 times (by Team 1 at T₁ and T₅).
- Station C: Visited 3 times (by Team 3 at T₁ and T₅, and by Team 4 at T₃).
- Station D: Visited 2 times (by Team 3 at T₂ and T₄).
- Station E: Visited 4 times (by Team 1 at T₃, Team 3 at T₃, and Team 4 at T₁ and T₅).

Adding the visits of Team 2 (which starts at A, visits F at T₁, E at T₂, F at T₃, and then returns to A):
- Station E gets at least 1 additional visit from Team 2 (at T₂), bringing its total to at least 5 visits.
- Station C gets at most 1 visit from Team 2, bringing its total to at most 4 visits.
- Station F gets at most 3 visits from Team 2, bringing its total to at most 3 visits.
- Station D is not visited by Team 2.

Comparing the totals, Station E is visited the largest number of times (at least 5 times).