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 identify the most frequently visited station, the patrol routes will be analyzed under the specified conditions:

1. Four teams (1, 2, 3, 4) conduct patrols from 09:00 to 12:00, commencing and concluding at Station A.
2. At 10:00, Teams 2 and 3 are located at Stations E and D, respectively.
3. At 10:30, Teams 1 and 3 are at Station E.
4. At 11:30, Teams 1 and 4 are at Stations B and E, respectively.
5. Team 4's routes exclude Stations B, D, and F. Only Teams 1 and 4 travel between A and E.

Based on this, the probable routes are derived:

• Team 1 utilizes routes A-E and A-B. Given its presence at E at 10:30 and 11:30, Station E is a frequent stop.
• Team 2 is at E at 10:00. A likely route is A-E-A, with potential variations for the return trip.
• Team 3 visits Stations D and E. Probable connections include A-D and a return via E.
• Team 4 travels only between A and E, avoiding B, D, and F. Its route is A-E.

Analysis indicates Station E is the most common destination:

• Team 1: Routes through E multiple times.
• Team 2: Visited E at 10:00 and may return via E.
• Team 3: Routes through E multiple times.
• Team 4: Route is exclusively A-E.

Consequently, Station E is confirmed as the most visited.

Answer 2

At 09:00, all four teams departed Station A via distinct routes, ensuring no street simultaneously hosted multiple teams moving in the same direction.

By 10:00, Team 2 was at Station E, and Team 3 was at Station D. Concurrently, only Team 1 and Team 4 traversed the segment between Stations A and E.

This indicates Team 2 proceeded to E via F, and Team 3 to D via C. At 10:30, only Teams 1 and 3 were at Station E. Team 4, avoiding B, D, and F, confined its movement to Stations A, E, and C.

Consequently, Team 4's sole feasible path to reach E by 11:30 was:

Route: (A → E → A → C → A → E → A)

Team 1's complete trajectory was:

Route: (A → B → A → E → A → B → A)

Team 3 returned to Station A by 12:00 via:

Route: (A → C → D → E → D → C → A)

Team 2 was restricted to the remaining 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

Station B was exclusively visited by Team 1, and this occurred on two occasions:

• At 09:30.
• At 11:30.

Therefore, the total number of visits to Station B is:

\[ \boxed{2} \]

Answer 3

To ascertain which team patrols the street linking Stations D and E at 10:15 hrs, a logical deduction based on the provided information is required:

• All teams commence their patrols from Station A at 09:00 hrs and conclude by 12:00 hrs.
• Each street traversal requires 30 minutes.
• Key data points are:
  1. At 10:00 hrs, only Teams 2 and 3 are present at Stations E and D, respectively.
  2. At 10:30 hrs, only Teams 1 and 3 are at Station E.
  3. At 11:30 hrs, Teams 1 and 4 are at Stations B and E, respectively.
  4. Teams 1 and 4 are responsible for patrolling the street connecting A and E.
  5. Team 4 does not operate in Stations B, D, or F.

Based on these facts, the following timeline is established:

• At 10:00 hrs:
  • Team 3 is located at Station D.
  • Team 2 is located at Station E.
• Given Team 3's presence at Station D at 10:00 hrs and the presence of Teams 1 and 3 at Station E at 10:30 hrs, it is inferred that Team 3 traveled from D to E between 10:00 hrs and 10:30 hrs.

Consequently, 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 depart from Station A via distinct routes.

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.

Deductions for routes at 10:00 a.m.:
Team 2 route: $A \rightarrow F \rightarrow E$
Team 3 route: $A \rightarrow C \rightarrow D$

At 10:30 a.m., Teams 1 and 3 are at Station E.
Team 4's movement is restricted to Stations A, E, and C, avoiding B, D, and F.
Potential paths for Team 4 to reach E by 11:30 a.m.:
- $A \rightarrow E \rightarrow A \rightarrow C \rightarrow A \rightarrow E$
- $A \rightarrow E \rightarrow A \rightarrow E \rightarrow A \rightarrow E$

However, Team 1 occupied the A–E path at 10:00 a.m., preventing Team 4 from using it then.
Therefore, Team 4's required path is: $A \rightarrow E \rightarrow A \rightarrow C \rightarrow A \rightarrow E$
At 12:00 p.m., Team 4 returns to A from E: $E \rightarrow A$

Team 4's complete 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 follows a loop: $A \rightarrow B \rightarrow A \rightarrow E \rightarrow A \rightarrow B \rightarrow A$
Team 2 has multiple path options, e.g.: $A \rightarrow F \rightarrow E \rightarrow F \rightarrow A$ or routes involving E multiple times.
Team 3's path: $A \rightarrow C \rightarrow D \rightarrow E \rightarrow D \rightarrow C \rightarrow A$
Only Team 4 passes through Station E exactly twice.

Correct Answer: 2

Answer 5

The objective is to determine the number of teams that traverse Station C daily. Based on the given conditions and operational structure, individual team routes can be deduced sequentially.

• All teams commence at Station A, must return by 12:00 hrs, and each street segment journey requires 30 minutes.
• Crucial Limitations:
  • Teams 2 and 3 are located at stations E and D, respectively, at 10:00 hrs.
  • Teams 1 and 3 are observed at station E at 10:30 hrs.
  • Teams 1 and 4 are positioned at Stations B and E, respectively, at 11:30 hrs.
  • Teams 1 and 4 exclusively utilize the street linking stations A and E.
  • Team 4 is prohibited from entering Stations B, D, or F.

Team-Specific Analysis:

• Team 1 repeatedly travels between A and E. It can reach C indirectly via routes that do not violate stated constraints.
• Team 2 is at E at 10:00 hrs and primarily operates on routes that do not conflict with other teams. It likely passes C when traveling beyond directly connected stations, possibly on a route such as A → C.
• Team 3, as stipulated, departs from D at 10:00 hrs. Its presence at E at 10:30 hrs necessitates transit through C when moving from D to E.
• Team 4 avoids routes through B, D, and F. Its operations are focused on efficient A → E routes. Therefore, it does not initially pass through C, but indirect paths may lead it there if allowed by other constraints.

Finding: Applying the established route restrictions, **Team 2 and Team 3** are confirmed to pass through Station C, either directly or indirectly, without violating any operational constraints. This leads to the final count of: **2 teams**.