Question

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

• A. Station F
• B. Station D
• C. Station E
• D. Station C
• A. Team 4
• B. Team 1
• C. Team 3
• D. Team 2
• A. 2
• B. 4
• C. 3
• D. 1

Answer 1

The Correct Option is C

To determine which station is visited the most times, we need to analyze the patrol routes based on the given conditions:

1. Four teams (Team 1, Team 2, Team 3, Team 4) patrol between 09:00 and 12:00, starting and ending at Station A.
2. Teams 2 and 3 are at Stations E and D at 10:00 hrs.
3. Teams 1 and 3 are at Station E at 10:30 hrs.
4. Teams 1 and 4 are at Stations B and E at 11:30 hrs. 
5. Team 4 never goes to Stations B, D, or F, and only Team 1 and 4 patrol between A and E.

Now let's derive the probable routes:

• Team 1 involves paths A-E and A-B:
  • From the information at 10:30 and 11:30, it frequently visits E.
• Team 2 is at E at 10:00:
  • Likely path: A-E-A, possibly returning via different routes.
• Team 3 is at D and E during its patrol:
  • Likely connections: A-D and back via E.
• Team 4 only reaches E, avoiding B, D, or F:
  • Route involves A-E.

Thus, most teams route through E:

• Team 1: Via E multiple times.
• Team 2: Visited E at 10:00 and possibly returns via E.
• Team 3: Via E multiple times.
• Team 4: Only visits A-E.

Conclusively, Station E is indeed the most visited.

Answer 2

At 9:00 a.m., all four teams selected different paths from the starting point (Station A) so that no street sees more than one team traveling in any direction at the same time. 

At 10:00 a.m., Team 2 is at Station E and Team 3 is at Station D. Also, only Team 1 and Team 4 patrol the street connecting Stations A and E.

This implies Team 2 reached E via F, and Team 3 reached D via C. Only Teams 1 and 3 are at E by 10:30 a.m. Team 4 avoids B, D, and F, so it must travel only through A, E, and C.

Therefore, Team 4's only viable path to reach E by 11:30 a.m. is:

Route: (A → E → A → C → A → E → A)

Team 1's full path is:

Route: (A → B → A → E → A → B → A)

Team 3 reaches A by 12:00 p.m. via:

Route: (A → C → D → E → D → C → A)

Team 2 must take the only available route: (A → F → E → F → A or E → F → A)

Final Movement Table

Teams	9:00	9:30	10:00	10:30	11:00	11:30	12:00
Team 1	A	B	A	E	A	B	A
Team 2	A	F	E	F	A / E	F	A
Team 3	A	C	D	E	D	C	A
Team 4	A	E	A	C	A	E	A

Conclusion

Only Team 1 passes through Station B, and it does so twice:

• At 9:30 a.m.
• At 11:30 a.m.

Therefore, the total number of times Station B is visited is:

\[ \boxed{2} \]

Answer 3

To determine which team patrols the street connecting Stations D and E at 10:15 hrs, let's logically deduce based on the given clues:

• The teams start from Station A at 09:00 hrs and return by 12:00 hrs.
• Each street takes 30 minutes to traverse.
• Important facts include:
  1. Teams 2 and 3 are the only ones at stations E and D respectively at 10:00 hrs.
  2. Teams 1 and 3 are the only ones at station E at 10:30 hrs.
  3. Team 1 and 4 are the only ones in stations B and E at 11:30 hrs.
  4. Team 1 and 4 patrol the street connecting A and E.
  5. Team 4 avoids stations B, D, and F.

From these facts, we break down the timings:

• At 10:00 hrs:
  • Team 3 is at Station D.
  • Team 2 is at Station E.
• Since Team 3 is at Station D at 10:00 hrs and Teams 1 and 3 are at Station E at 10:30 hrs, Team 3 travels from D to E between 10:00 hrs and 10:30 hrs.

Thus, Team 3 patrolled the street connecting Stations D and E at 10:15 hrs.

Answer 4

Given: 
At 9:00 a.m., all four teams have selected distinct paths from the starting point (Station A), ensuring no two teams are on the same street simultaneously.

At 10:00 a.m.:
- Team 2 is at Station E.
- Team 3 is at Station D.
- Only Team 1 and Team 4 use the street connecting A and E.

So, Team 2 must have taken the route: $A \rightarrow F \rightarrow E$
Team 3 must have taken the route: $A \rightarrow C \rightarrow D$

At 10:30 a.m., only Teams 1 and 3 are at Station E.
Team 4 avoids B, D, and F, so it can only go through A, E, and C.
Possible paths for Team 4 to reach E by 11:30 a.m. are:
- $A \rightarrow E \rightarrow A \rightarrow C \rightarrow A \rightarrow E$
- or $A \rightarrow E \rightarrow A \rightarrow E \rightarrow A \rightarrow E$

But since Team 1 is using the A–E path at 10:00 a.m., Team 4 cannot use it then.
Therefore, Team 4 must use: $A \rightarrow E \rightarrow A \rightarrow C \rightarrow A \rightarrow E$
Finally, at 12:00 p.m., Team 4 returns to A: $E \rightarrow A$

Team 4 full path: $A \rightarrow E \rightarrow A \rightarrow C \rightarrow A \rightarrow E \rightarrow A$

Team Movement Table:

Team	9:00	9:30	10:00	10:30	11:00	11:30	12:00
1	A	B	A	E	A	B	A
2	A	F	E	F	A/E	F	A
3	A	C	D	E	D	C	A
4	A	E	A	C	A	E	A

Team 1 also follows a loop to B: $A \rightarrow B \rightarrow A \rightarrow E \rightarrow A \rightarrow B \rightarrow A$
Team 2 has options like: $A \rightarrow F \rightarrow E \rightarrow F \rightarrow A$ or via $E$ again.
Team 3 goes: $A \rightarrow C \rightarrow D \rightarrow E \rightarrow D \rightarrow C \rightarrow A$
Only Team 4 passes through Station E exactly twice.

Correct Answer: 2

Answer 5

The problem involves determining how many of the four teams pass through Station C in a day. Given the constraints and logistical setup, we can unravel the paths of each team step by step.

• All teams start at Station A and return by 12:00 hrs, with each street transit taking 30 minutes.
• Key Constraints:
  • Teams 2 and 3 are at stations E and D at 10:00 hrs respectively.
  • Teams 1 and 3 are at station E at 10:30 hrs.
  • Teams 1 and 4 are at Stations B and E at 11:30 hrs respectively.
  • Team 1 and Team 4 exclusively patrol the street connecting stations A and E.
  • Team 4 can't pass through Stations B, D, or F.

Team Analysis:

• Team 1 must travel A → E multiple times and can pass through C indirectly by other routes not contradicting constraints.
• Team 2 is at E at 10:00 hrs and primarily covers routes that avoid clashing with other teams. It likely passes C when moving anywhere further than connected stations, potentially A → C.
• Team 3, by requirement, starts from D at 10:00 hrs, and being found at E at 10:30 hrs must pass via C when transiting from D to E.
• Team 4 avoids paths containing B, D, F, and must be directly efficient with A → E routes, thus not passing C initially, but can pass through due to indirect routes allowed.

Conclusion: Following the logical path restrictions, Team 2 and Team 3 are the confirmed teams passing through Station C directly or indirectly according to allowed paths without contradicting constraints, making the answer: 2 teams.