# Fire exit

The Binks method of fire rescue consists simply of a rope that passes through a pulley and has at each end a large basket. When one of the baskets goes down, the other goes up. In this way, by placing an object in one of the baskets to serve as a counterweight, a heavier object can be lowered into the other basket. The inventor says that his device must be hung on the outside of all the buildings in the world.

The system was adopted in a hotel, but the most savvy guests used it to escape overnight without paying, so the mechanism did not continue to have the approval of the hoteliers.

The image shows a Binks elevator located in front of the window of a modern summer hotel. Nothing that weighs more than thirty pounds can be safely dropped in one basket while the other is empty and thirty pounds is the safety limit of the difference that can exist between both baskets when the two carry a weight.

One night a fire broke out in the hotel and all guests managed to escape except the night watchman and his family. When they could be alerted, all escape routes, except the Binks elevator, were blocked by fire. The watchman weighed 90 pounds, his wife 210 pounds, the dog 60 pounds and the baby 30 pounds.

Each basket has enough capacity to house all four and weights are not available for use in the baskets, only the man, his wife, the dog and the baby.

If we assume that neither the dog nor the baby are able to enter or leave the basket without the help of the man or his wife, What is the fastest way for the four to be safe?

#### Solution

The fastest method of getting everyone down the Binks elevator is as follows:

• Lower the baby in a basket and the other goes up empty.
• Lower the dog in one basket and raise the baby in the other.
• Lower the man in one basket and raise the dog in the other.
• Lower the baby in a basket and the other goes up empty.
• Lower the dog in one basket and raise the baby in the other.
• Lower the baby in a basket and raise the other empty.
• Put the wife down in one basket and everyone else in the other.
• Lower the baby in a basket and raise the other empty.
• Lower the dog in one basket and raise the baby in the other.
• Lower the baby in a basket and raise the other empty.
• Lower the man in one basket and raise the dog in the other.
• Lower the dog in one basket and raise the baby in the other.
• And finally lower the baby in a basket and up the other empty.