# It’s magic

Anil Kumar Patnaik

As promised, Abhas sir entered the classroom. He asked one of the children to give him their English literature book.
“English literature book?” the children asked.
“You wanted to see magic, right?”
“Yesss…,” the reply came in chorus. Abhas sir then took out few papers from his pocket, turned the pages of the literature book, scribbled something on the papers and put them back in his pocket.
“Okay, open your books,” Abhas sir instructed.
“Write any three digit number abc, such that a-c is greater than or equal to 2, for example you can write 765, where 7-5=2 or 974 where 9-4=5,” he added.

Children then looked at him for his next instruction.
“Now write the digits of the number in ascending and descending order, for example if you have chosen 849, you will write 984 and 489”. This was clear to the children.
“Now subtract the smaller number from the bigger number and keep the result.”

The children were getting excited.
“Now, reverse the number and add it to the result. For example, if your result is 468, its reverse is 864. Add both these numbers and keep the result. Please do not show it to anyone.”

The children were listening to his instructions with rapt attention.
“I am sure the result of your exercise is a four-digit number,” Abhas sir told everyone.
“Yes sir…” the children responded.
“Take out your English literature books, open the page number that is same as the first three digits of the number you have come up with. Then, proceed to the line equal to the fourth digit, for example if your answer is 2167, open page number 216 and go to the seventh line. Please note down the line in your notebook.”

Abhas sir’s explanations were very clear and lucid.

A few children continued with their task, while those who were done with their answers awaited the next set of instructions.

“Okay, those who have finished can come in a line,” Abhas sir said with a smile. And as the first child came with his copy, Abhas sir took out one of the papers he had scribbled on earlier from his pocket and handed it to the child. “Oh my God!” cried the child when he found that Abhas sir had written the same line at the beginning of the period that he had written after the mathematical calculations. Absolute bewilderment was conspicuous on his face. Came the second child, “My goodness,” he was perplexed yet happy.

Each of them came to him to see the lines which they had written were the same as those by Abhas sir. The children were so amused and stunned that they did not notice either the bell ringing or Abhas sir leaving the class.

Just then Mr. Sharma, the school principal invited Abhas sir to his room. Abhas sir entered the principal’s chamber and was offered a seat. “I was on my rounds and observed your class. Quite interesting. Please explain how you performed the trick.” Mr. Sharma asked Abhas sir. “Sir, since a, b, and c are the three digits of the original number, the number is 100a+10b+c, on reversing, the number is cba, that is 100c+10b+a. When subtracted (100a+10b+c) – (100c+10b+a) is 99a-99c, that is 99(a-c). In the beginning itself I had made it clear that, in the three-digit number abc, (a-c) must be 2 or more. [The reason is to avoid palindromic numbers (like 212, 333, 919 etc) and two digit numbers (for example 201, if reversed it is 102. 201-102 = 99.)]

Hence the number became 99×2=198, on reversing, we get 891. 198+891=1089, 99×3=297. on reversing it’s 792. 297+792=1089 and similarly the other numbers 396,495,594,693,792,891, whose sum, on reversing and adding with the original number, results 1089. Any of the numbers if reversed and added to itself will be equal to 1089, that is 198+891=1089, 297+792=1089 and so on. This is simple mathematics sir,” explained Abhas. “That’s fine but how did the lines you had written match with the lines by children?” Mr Sharma continued. Abhas sir took out the papers which were still in his pocket and showed them to Mr. Sharma, “and a genius was born.” was written in each of the papers.

“I have written the same thing in each paper; it is the ninth line on page 108 in their English literature book and each of the children was getting 1089 as their answer. I ruffled the pages just to beguile them,” replied Abhas sir and stood up.

As he took permission to leave, Mr. Sharma looked at him with appreciation.

The author is an enthusiastic educator of mathematics and writes on topics related to innovative and engaging educational methods. He is a CBSE resource person for teacher professional development programmes. He is known for his creative skills, story writing, dramatic and mimicry abilities, disciplined lifestyle, and contributions as a community worker. He can be reached at anilpatnaik8@gmail.com.