A farmer challenges an engineer, a physicist, and a mathematician to fence off the largest amount of area using the least amount of fence. The engineer made his fence in a circle and said it was the most efficient. The physicist made a long line and said that the length was infinite. Then he said that fencing half of the Earth was the best. The mathematician laughed at the others and with his design, beat the others. What did he do?
The mathematician made a small circular fence around himself and declared himself to be on the outside.
I look flat, but I am deep,
Hidden realms I shelter.
Lives I take, but food I offer.
At times I am beautiful.
I can be calm, angry and turbulent.
I have no heart, but offer pleasure as well as death.
No man can own me, yet I encompass what all men must have.
A farmer is travelling with a fox, a sheep and a small sack of hay. He comes to a river with a small boat in it. The boat can only support the farmer and one other animal/item. If the farmer leaves the fox alone with the sheep, the fox will eat the sheep. And if the farmer leaves the sheep alone with the hay, the sheep will eat the hay.
How can the farmer get all three as well as himself safely across the river?
The farmer takes the sheep across the river, then returns back.
The farmer takes the fox across the river.
The farmer takes the sheep back to the first side of the river.
The farmer leaves the sheep back on the first side of the river, and takes the hay to the other side.
The farmer returns to the first side of the river.
The farmer brings the sheep back to the second side.