A farmer has a dog, two geese and three bags of corn. He comes to a river. The boat to ferry him across the river can only hold the man plus two of his six possessions at a time. The farmer knows that if he is not right there the dog will eat a goose or a goose will eat the corn. How many time does the farmer need to cross the river to get all of his possessions safely to the other side?
3 times
It will take more than three trips. You'll need to bring at least one of the passengers back to the original shore.
To determine how many times the farmer needs to cross the river to bring all his possessions safely to the other side, we need to carefully analyze the constraints and plan the crossings. Let's break it down step by step:
1. The farmer starts by taking the two geese across the river, leaving the dog and the three bags of corn on the original side. This is the first crossing.
2. The farmer then returns alone to the original side to pick up another possession. He leaves the dog behind on the other side to ensure it doesn't eat the geese or the corn. This is the second crossing.
3. The farmer picks up one of the remaining possessions (either the dog or one bag of corn) from the original side and takes it across the river. However, he needs to be careful not to leave the dog alone with the geese on the other side. So, he brings the dog back to the original side with him. This is the third crossing.
4. Now, the farmer takes the other two possessions (either the dog or one bag of corn, whichever he left behind) across the river, leaving one possession on the other side. This is the fourth crossing.
5. The farmer returns alone to the original side to get the remaining possession (either the dog or one bag of corn). He leaves the dog behind on the original side to avoid any conflicts. This is the fifth crossing.
6. Finally, the farmer brings the last possession across the river, completing the sixth and final crossing.
So, in total, the farmer needs to cross the river six times to safely transport all his possessions to the other side while ensuring the dog doesn't eat the geese or the geese eat the corn.