In a room, there are some chairs and some people. If on each chair, only one person is seated, then there is no chair for exactly one person. If on each chair, two persons sit, then there is one vacant chair. What is the number of chairs in the room?

Question

Accepted Answer

Let the number of chairs be C and the number of people be P.

1. If one person sits on each chair, then there is no chair for exactly one person. This means one person is left without a chair:
   P = C + 1

2. If two persons sit on each chair, then there is one vacant chair. This means one chair is empty:
   Number of chairs occupied = C - 1
   Since two persons sit on each occupied chair:
   P = 2 * (C - 1) = 2C - 2

From the two equations:
   P = C + 1
   P = 2C - 2

Equate:
   C + 1 = 2C - 2
   1 + 2 = 2C - C
   3 = C

Therefore, the number of chairs is 3.

Answer

Answer

Answer