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A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially.

What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?

Top view of a building divided into rooms by walls, with four doors marked; P is in the long room along the bottom and Q is in the upper right room

  • A.4
  • B.3
  • C.2
  • D.1

Answer: C

The minimum number of doors to open is 2.

P is in the long room along the bottom of the building. The wall above it has only one door, at its left end, so the first door opened is that one, leading into the room on the left above it. That room has a door in its right-hand wall, leading into the large room on the right, and that room is open to Q’s room through the gap at the right end of the short wall between them. So the route P, bottom-left door, middle door, then through the gap to Q opens two doors.

One door is not enough, because no single door connects P’s room to a room open to Q. The two upper doors lead into and out of the small central room and are not needed; a route through them would open three or four doors, the distractors.

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