Terms & Conditions
He has one mile of fence, with which to surround the horses.
Luckily there is a very straight river which he can also use.
Obviously the farmer wants to fence off as much land as possible, what shape will the fenced off area be and how large?
Hint: You might need to remember the formula for the area of a circle (= Pi x radius x radius)
The fenced off area will be a large semicircle, with the river forming the diameter of the circle and the area will be 0.16 of a square mile.
As the fence forms the curved semicircle section, so half the circle has a length around of 1 mile (the fence), so the whole circle has a circumference of 2 miles. As circumference = Pi x diameter, then diameter = circumference / Pi. In this case the diameter is therefore 2 / Pi and the radius is therefore 1 / Pi.
The area of the entire circle would be Pi x (1 / Pi) x (1 / Pi) = 1 / Pi.
We only want half of this area, so the answer is 1 / (2 x Pi) = 0.16 of a square mile.
Note: if the farmer were to make a square area (using the river as one side), each side would be 1/3 of a mile, and 1/3 x 1/3 = 0.11 of a square mile, which is smaller.
In the town of Biddulph, 7% of all telephone subscribers are ex-directory.
If you pick 500 people at random from the telephone directory, how many will have ex-directory numbers?
Hint: This is a Gotcha.
They are ex-directory, and therefore are not in the directory!