Go, Figure it Out!

“Want to see some number magic?” my grandfather had asked.

“Yes, Bauji!” I had rushed over to him.

“Enter any three-digit number in your calculator and do not let me see it.”

That is when I had first entered 342.

“OK. Now enter the same number again, so you have a six-digit number,” he had said.

I punched in 342 again, so now I had 342342 entered in my calculator.

“Now, I do not know the number you have in there, Ravi, but I do know that it is evenly divisible by 13.”

By “evenly divisible” he meant that there would be no remainder. For example, 9 is evenly divisible by 3 but not by 4. Bauji’s claim seemed fantastic to me. How could he know that my number, randomly chosen and completely unknown to him, would be evenly divisible by 13? But it was!

I divided 342342 by 13 and I got 26334 exactly, with no remainder. “You’re right,” I said, amazed.

He wasn’t finished, though. “Now, Ravi, I also know that whatever number you got after you divided by 13 is further divisible by 11.” He was right once again. 26334 divided by 11 was 2394. Why was this working?

“Take the number you got and divide by 7. Not only will it divide evenly, but you will be surprised at what you get.” He had begun his pacing and I knew that he was as excited as I was. I divided 2394 by 7 and I got 342!

“Oh! Oh! It’s the number I started with! Bauji, how did this happen?”

My grandfather just sat there, grinning at the completeness of my astonishment.

“You will just have to figure that one out Ravi.”

***

Does it work for any 3 digit number you start with? Why/why not? Go, figure it out!


This excerpt is taken from 'A Certain Ambiguity' written by Gaurav Suri & Hartosh Singh Bal.

This book won the 2007 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers. 

You can read the entire novel from here

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