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Kiriti M.'s problem wrong answer?

Kiriti's number URL: https://brilliant.org/mathematics-problem/kiritis-number/?group=kI5dClibjr16#!/solution-comments/5492/

While reading up the solutions to this question, I discovered that John Aries Lopez comment that 111...(12 times) satisfies the equation and therefore N = 1122334456 which means the digit sum is 31. So isn't the answer suppose to be 31??

But if that is the case, then the divisibility test of 9 is not accurate. 111...(12 times) does not sum up to a value divisible by 9...but it is divisible by 9!

Note by Shaun Loong
3 years, 10 months ago

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First of all you must correct your typo that instead of 9 it should be 99 according to the original question. And I have also seen John's comment but I think he might have made some mistake while calculating the division process as it is wrong that 111...(12 times) is divisible by 99 because it gives quotient as 1122334455.666666666666666666667. And 1122334455667789 when multiplied with 99 it gives 111...(18 times). You can check it by yourself.

Shubham Kumar - 3 years, 10 months ago

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Ahaha I see I see! Thanks for clearing up my confusion! :)

Shaun Loong - 3 years, 10 months ago

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If you read Christian's reply to that comment, you will see that John made an inaccurate statement.

I believe that John's error was made when he tried to use a calculator, and got hit by the rounding.

Calvin Lin Staff - 3 years, 10 months ago

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That's my pleasure !!!

Shubham Kumar - 3 years, 10 months ago

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