A kennel only has 76 rooms to house dogs in. What is the minimum number of digs needed in order to guarantee that at least two dogs have to share a room at the kennel?
The pigeonhole principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. In this case, the "pigeons" are the dogs and the "pigeonholes" are the rooms in the kennel.
Since there are only 76 rooms in the kennel, if there are more than 76 dogs, then at least two dogs will have to share a room. Therefore, we need at least 77 dogs in order to guarantee that at least two dogs will share a room.