You can take the goat to the field, but can’t make it graze half the area. At the interview, Napoleon Bonaparte was taken to a circular field of unit radius and it was fenced in. He was asked to tie a goat to a point on the interior of the fence with a chain of certain length and you had to tell what length of chain must be used in order to allow the goat to graze exactly half the area of the field.

I always wondered how could such a beautiful mind as Napoleon Bonaparte turn to war. Then, I found something what John Adams had said in 1790 and got my answer, so, I produce the quote here. Napoleon made not only war strategies, but also beautiful theorems of mathematics. There is a theorem called Napoleon’s Theorem, which states that if we construct equilateral triangles on the sides of any triangle (all outward or all inward), the centers of those equilateral triangles themselves form an equilateral triangle.The theorem can be generalized to say that the centers of regular n-gons constructed on the sides of a regular n-gon form a regular n-gon, and naturally it also applies to n-gons subjected to conformal and affine transformations. This is said to be one of the most-often rediscovered results in mathematics. The earliest appearance of this theorem is in an 1825 article by Dr. W. Rutherford in ‘The Ladies Diary’.

Mathematicians of his age have said: "The possibility of Napoleon knowing enough geometry for this feat is as questionable as the possibility of his knowing enough English to compose the famous palindrome: ABLE WAS I ERE I SAW ELBA."

The answer to the goat problem could be had from one of Napoleon’s many biographies; and I say that if the radius of the field is of unit 1, the length of the rope should be nothing less than 1.15872847 units for the goat to graze exactly half the area. This problem was the Waterloo of many readers and many left the battlefield midway. The person who has reached the closest to this answer is Rajeev Kumar Tak, who gives the figure to be 1.15873, without telling us how he arrived at it. The answer according to Shubhangi Arora is: 2^ ½ x radius of the circle. "The length of the rope should be .707 of the radius of the circular field," says Ravinder Mittal. Karan Rishi says: "The goat should be tied in the centre of the field with a chain of radius 1/root2 times radius of field." Ranjeet Singh Matharu says: "If the radius of field is = x, then, the goat is tied to any point inside the field so that the radius is x/root(2)." Get up and fight again. Keep writing at The Tribune or adityarishi99@yahoo.co.in.