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Fruits and Noughts

The arithmetic class was in progress. "If I divide 5 bananas among 5 students how many bananas will each one get?" asked the teacher.
"One!" shouted a boy.
"Right," said the teacher. "And if I distribute 1000 bananas among 1000 children how many will each child get?"
"Excuse me, sir," said a boy, raising his hand for permission to speak. "If no bananas are distributed among no students will everyone still get one banana?"
The class burst into laughter. The teacher rapped on the table with his cane.
"Silence!" he said.
The boys fell silent.
"There's nothing wrong with the question he has asked," said the teacher. "I will tell you the answer. If zero bananas is divided among zero students, each will get an infinite number of bananas!"
The students didn't understand. The teacher however complimented the boy on his question. He had realised that his student was exceptionally bright. It had taken mathematicians several centuries to answer the question the boy had asked. Some said zero divided by zero was zero; others that zero divided by zero was unity (one).
It was Bhaskara who finally showed that zero divided by zero was infinity.
The boy who had asked the question was Srinivas Ramanujan, one of the greatest mathematicians India has produced.
When the famous mathematician Kari Gauss was a schoolboy in Germany his teacher one day asked the class to add up all the numbers from 1 to 100 and to try to do it in ten minutes.
Within 30 seconds Kari put up his hand.
"Yes, Kari?" said his teacher. "What is it? Didn't you understand the problem? What you have to do is..."
"Yes, sir," interrupted Gauss. "I know and I've got the answer."
"You've got the answer?" said his teacher. "But you've not even written down the numbers. What you have to do is write down all the numbers from 1 to 100 one below the other and then..."
"There's no need for that, sir," said the boy. "You see, sir, the first number 1, added to the last number gives 101; the second number 2 added to the second last number gives 101; the third number 3 added to the third number from the other end also gives 101. So do all the other pairs. As there are 50 pairs of 101 all you have to do is multiply 101 by 5 and add zero to get the answer 5050."
The teacher could only gape because the answer was correct.

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