If you experience any problems accessing the site using HTTP, you can try HTTPS by clicking the link on the left.


Privacy Policy  -  Terms & Conditions  -  See Details
This website uses cookies. By using this website you are accepting the use of cookies.
For more information please view our privacy policy.

BB Logo

Difficulty: MediumPuzzle Details

Puzzle IconA local farmer wants to keep his horses safe.

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?

[Ref: ZLHI]

Show Hint Show Answer Print Puzzle
Direct Link:

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.

Our Favourite Illusions

 Shadow Illusion
Are the squares A and B the same colour?

 Spinning Dancer
Which way is the dancer spinning?

 Impossible Waterfall?
Is the water flowing uphill in this impossible waterfall?

 The Butterfly
A colourful butterfly?

 Duck Or Rabbit?
Is this a duck or a rabbit?

 Hidden Faces
Can you find his three daughters as well?

 Blind Spot
An amazing demonstration of your blind spot.

 Impossible Prongs?
Impossible prongs?

 What Am I?
Can you tell what this is a picture of?

 Who Turned To?
Who is missing?

 Same Eyes?
Are her eyes the same colour?

 Parallel Cafe Wall Lines?
Are the horizontal lines parallel?




BrainBashers™ is a trademark. This website uses cookies. By using this website you are accepting the use of cookies. For more information please view our privacy policy. By using this website you are also agreeing to our terms and conditions.