Math or magic?

Number Theory Level 3

Here is a dialogue between Himu an Rupa:

"Rupa, write a huge number in your pad where all the digits are not same. "

"OK. Now? "

"Now rearrange the numbers as your wish. You can add some 0 to make this game more difficult for me. "

"Then? "

"Now you have two numbers. Subtract the small number from the bigger one. "

"Emm..... Now? "

"Now sum up all the digits of your result except one digit and tell me the answer . "

"It's 473 ."

"You have omitted ß . Am I right or am I right?"

"Oh... Right you are !But how is this possible? "

Himu didn't give the answer; only smiled.

What is the value of ß ? Can you explain it?


The answer is 4.

Arifin Ikram by arifin ikram , 17, Bangladesh

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2 solutions

The result after performing the subtraction will be a multiple of 9 9 . Hence the digit sum will also be a multiple of 9 9 . The digit sum of 473 473 is 14 14 . Since the required digit is a single digit number, therefore that digit is 18 − 14 = 4 18-14=\boxed 4 .

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Arifin Ikram
Sep 26, 2019

The result obviously will be a multiple of 9 9 . We know, the numbers who are divisible by 9 9 , the sum of their digits will be divided by 9 9 . Here, the sum is 14 14 . Greater than it but nearest multiple of 9 9 is 18 18 .

So our answer will be 18 − 14 18-14 = 4 \boxed{4}

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The thing we have to find is nowhere in the question.

Also 'Am I right or I am right'

Mr. India - 1 year, 7 months ago

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