Math Puzzle

Many years ago, a cruise liner sank in the middle of the Pacific Ocean. The survivors luckily landed on a remote desert island. There was enough food for the 220 people to last three weeks. Six days later a rescue ship appeared, unluckily this ship also sank, leaving an additional 55 people stranded on the island to now share the original rationed food. The food obviously had to be re-rationed, but everyone was now on one-half of the original ration, so how many days in total would the food last for, from the day of the original sinking?

Farmer,Goat and Wolf

A farmer is standing on one side of the river and with him are a wolf, a goat and a box of cabbages. In the river there is a small boat. The farmer wants to cross the river with all the three items that are with him. There are no bridges and in the boat there is only room for the farmer and one item.
If he leaves the goat with the cabbages alone on one side of the river the goat will eat the cabbages. If he leaves the wolf and the goat on one side the wolf will eat the goat. Only the farmer can separate the wolf from the goat and the goat from the cabbage
How can the farmer cross the river with all three items, without one eating the other?

8 Ball Puzzle

The problem is quite simple. You are given 8 identical-looking balls, one of which is heavier than the other 7 (all of which weigh the same). Using an old-fashioned mechanical set of scales you must identify the heavier ball using the scale as few times as possible. The scale is constructed using two bowls and an arm enabling the bowls to either balance or have one bowl rising while the other (and heavier bowl) falling. Out of these 8 balls you have to find heavier ball in 2 chances.