Problems, puzzles and mechanical puzzles

We begin by taking a look at some classic puzzles, such as the wolf, the goat and the cabbage, and the water jug puzzles.

The wolf, the goat and the cabbage

Puzzles go back centuries. One of the most well-known puzzles is the ‘wolf, the goat and the cabbage’ puzzle that dates back to at least the 9^th century.

The puzzle is as follows. A farmer goes to market and buys a wolf, a sheep and a cabbage. On his way home, he has to cross a river by boat from one side to the other. The boat can carry only the farmer and one other thing – the wolf, the goat or the cabbage, so the farmer will need to make a few trips to boat all three over to the other side. During the boating, he will always have to leave two things on their own on the banks of the river. For obvious reasons, the wolf cannot be left alone with the goat – he will devour it. The goat cannot be left with the cabbage, because she will eat it. How then, can the farmer transfer all three to the other side of the river, leaving them all intact?

The wolf, the sheep and the cabbage – solution

Obviously, the farmer should first take the goat over, leaving the wolf with the cabbage. He then returns alone to boat over either the cabbage or the wolf. It really doesn’t matter which. Let’s assume that he takes the wolf. He cannot leave the wolf with the goat while he returns for the cabbage, so he leaves the wolf and carries the goat back to the original bank with him. He leaves the goat and picks up the cabbage, boating it over and leaving it on the far-side bank with the fox. Finally, he returns alone to transport the goat over to the other bank.

Here is another well-known, medieval problem, also known as the ‘water pouring puzzle’.

The water jug puzzle

You have an 8 litre jug full of water and two smaller jugs, one that contains 5 litres and the other 3 litres. None of the jugs have markings on them, nor do you have any additional measuring device.You have to divide the 8 litres of water equally between your two best friends, so that each gets 4 litres of water. How can you do this?

The water jug puzzle – solution

• First, water is poured from the 8 litre jug into the 5 litre jug, leaving 3 litres of water in the original 8 litre jug.
• Next, water is poured from the 5 litre jug into the 3 litre jug, so we now have 3 litres of water in the 8 litre jug, 2 litres of water in the 5 litre jug and 3 litres of water in the 3 litre jug.
• The 3 litre jug is emptied into the 8 litre jug, so the 8 litre jug now contains 6 litres of water.
• The 2 litres of water in the 5 litre jug are now poured into the empty 3 litre jug.
• Water is poured from the 8 litre jug (which at this stage contains 6 litres) into the empty 5 litre jug.
  We now have 5 litres of water in the 5 litre jug, 2 litres of water in the 3 litre jug and 1 litre of water in the 8 litre jug.
• Water is poured from the 5 litre jug to fill the 3 litre jug which already contains at this stage 2 litres of water.
• We are left with 4 litres of water in the 5 litre jug which is given to one friend, and 3 litres of water in the 3 litre jug that is poured back into the 8 litre jug that already contains 1 litre of water. This gives 4 litres of water which are given to the second friend.

Some mechanical puzzles