Puzzle of renting rooms

3dpuzzlerecreational-mathematics

I have a doubt in this question :- How many students turned up for renting the rooms? , for convenience I have posted the same question below also

Sara has a house which she wants to convert to a hostel and rent it out to students of a nearby women’s college. The house is a two story building and each floor has eight rooms. When one looks from the outside, three rooms are found facing North, three found facing East, three found facing West and three found facing South. Expecting a certain number of students, Sara wanted to follow certain rules while giving the sixteen rooms on rent:

All sixteen rooms must be occupied.

No room can be occupied by more than three students.

Six rooms facing north is called north wing. Similarly six rooms facing east, west and south are called as east wing, west wing and south wing. Each corner room would be in more than one wing. Each of the wings must have exactly 11 students. The first floor must have twice as many students as the ground floor.

However Sara found that three fewer students have come to rent the rooms. Still, Sara could manage to allocate the rooms according to the rules.

How many students turned up for renting the rooms?

  1. 24

  2. None of these

  3. 27

  4. 30

  5. 33

I am not able to visualize the whole setup of building, there are 8 rooms on each floor , and there are 2 floors which means 16 rooms.

Now the orientation part is confusing me a lot, the question says "When one looks from the outside, three rooms are found facing North, three found facing East, three found facing West and three found facing South. " which gives a total of 12 rooms , but we know that we have 16 rooms in the building.

Also how is the wing system being designed, it would be really nice if someone could help me out with a 2-D or a 3-D figure for the setting , so that I can give a try to this question

This is what I have been able to imagine for a floor ?:-

enter image description here

Here R1, R2, R3 are facing north; R4, R5, R6 facing east; R7,R8,R9 facing south and R10,R11,R12 facing west, this counts to 12 rooms alone per floor , but there are only 8 rooms as per question

Best Answer

This is how the rooms on floor $1$ are arranged:

+--------+--------+--------+         N
| Room 1 | Room 2 | Room 3 |         ^
+--------+--------+--------+         |
| Room 4 |        | Room 5 |   W <---+---> E 
+--------+--------+--------+         |
| Room 6 | Room 7 | Room 8 |         v
+--------+--------+--------+         S

There are three rooms facing north: rooms 1, 2 and 3.
There are three rooms facing east: rooms 3, 5 and 8.
There are three rooms facing south: rooms 6, 7 and 8.
There are three rooms facing west: rooms 1, 4 and 6.

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