What is a river crossing puzzle? It is a type of puzzle in which the object is to carry items from one river bank to another, usually in the fewest trips. The difficulty of the puzzle may arise from restrictions on which or how many items can be transported at the same time, or which or how many items may be safely left together.
This topic contains tasks devoted to various difficult situations related to the crossing of any creatures or objects. In this case, you have to come up with some way or algorithm to do this. Typically, such algorithms are called maneuvers by analogy with the maneuvering of troops, ships, convoys, etc.
In crossing tasks you need to transport something or someone somewhere or change places, observing some rules. For example, the simplest maneuvering exercise is to arrange three balls in reverse order, if you can change the two adjacent ones:
The solution is extremely simple - we change the balls one by one until we get what we want. For example, like this:
1. On one bank of a river, there are three lions and three bulls. There is one boat available that can hold up to two animals, and they would like to use it to cross the river. If the lions ever outnumber the bulls on either of the river's banks, the bulls will get eaten. How can the boat be used to safely carry all three bulls and three lions across the river?
2. There are 4 persons (A, B, C, and D) who want to cross a bridge at night.
A takes 1 minute to cross the bridge.
B takes 2 minutes to cross the bridge.
C takes 5 minutes to cross the bridge.
D takes 10 minutes to cross the bridge.
There is only one torch with them, and the bridge cannot be crossed without the torch. There cannot be more than two persons on the bridge at any time, and when two people cross the bridge together, they must move at the slower person's pace. Can they all cross this bridge in no more than 17 minutes?
3. A farmer wants to cross a river and take with him a wolf, a goat, and a cabbage. There is a boat that can fit himself plus either the wolf, the goat, or the cabbage. If the wolf and the goat are alone on one shore, the wolf will eat the goat. If the goat and the cabbage are alone on the shore, the goat will eat the cabbage. How can the farmer bring the wolf, the goat, and the cabbage across the river?
4. A detachment of 25 soldiers must cross a wide and deep river with no bridge in sight. They notice two 12-year-old boys playing in a rowboat by the shore. However, the boat is so tiny that it can only hold two boys or one soldier. How can the soldiers get across the river and leave the boys in joint possession of the boat?
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