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]
Given : At 9:00 a.m., it's understood that all four teams have selected distinct paths from the starting point since no street sees more than one team traveling in any direction simultaneously. At 10:00 a.m., we know Team 2 is at station E, and Team 3 is at station D. Moreover, only Team 1 and Team 4 patrol the street connecting stations A and E. This scenario is only possible if Team 2 traveled from A to E through F, and Team 3 arrived at station D via station C. Also, it's confirmed that only Teams 1 and 3 are at Station E by 10:30 a.m., and Team 4 avoids passing through Stations B, D, or F. Consequently, Team 1 likely opted for the (A-B) route initially, while Team 4 likely selected the (A-E) route at 9:00 a.m. So, Team 1 is expected to arrive at B by 9:30 a.m., return to A by 10:00 a.m., and then proceed to E by 10:30 a.m. Given that Team 4 avoids stations B, D, and F, they can only travel through stations A, E, and C. Therefore, Team 4's routes to reach station E by 11:30 could either be (A-E-A-C-A-E) or (A-E-A-E-A-E). Given that Team 1 is already en route from A to E at 10:00 a.m., Team 4 cannot opt for the same route at that time. Therefore, the definitive route for Team 4 to reach E by 11:30 a.m. is (A-E-A-C-A-E), and by 12:00 p.m., Team 4 will return to station A. Therefore, the complete route map for Team 4 is (A-E-A-C-A-E-A).
Teams
9.00
9.30
10.00
10.30
11.00
11.30
12.00
1
A
B
A
E
2
A
F
E
3
A
C
D
4
A
E
A
C
A
E
A
Observing that Team 1 arrives at station E by 10:30 a.m., we note that they will reach station B by 11:30 a.m., indicating they must travel to B via A. Therefore, the complete route plan for Team 1 is (A-B-A-E-A-B-A). Additionally, it's confirmed that Teams 1 and 3 are the sole occupants of station E at 10:30 a.m.
Teams
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
3
A
C
D
E
4
A
E
A
C
A
E
A
At 10:00 a.m., Team 2 has only one option: they must go from E to F since Team 3 is already on the E to D route. For Team 3 to reach A by 12:00 p.m., their only feasible route is E-D-C-A.
Teams
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
3
A
C
D
E
D
C
A
4
A
E
A
C
A
E
A
So, At 10:30 a.m., Team 2's possible routes back to A are either (F-A-F-A) or (F-E-F-A). Therefore, the final table is as follows :
Teams
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
From the data available in the above table , we can see that the teams have crossed the B Station 2 times in the given time period.
