You need more than maths

Number Theory Level pending

526315789473684210 multiplied by any number BETWEEN ? and ?? will result in the digits starting at a different point (there's also an extra 0 behind). So, what are ? and ?? respectively? (if your answer is something like 1 and 10 you put the first number, then the second number, i.e. 110, 2 and 19 you put 219 and so on...)


The answer is 218.

Jian Yi Lee by Jian Yi Lee , 19, Singapore

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1 solution

Jian Yi Lee
Aug 30, 2015

This obviously does not work on 1, and if you work it out, you will find that you can do this with numbers from 3 to 17. This is also between 2 and 18. Of course you are going to spend lots of time to find it :)

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Is there a way to do it without trying all values and checking which works? How can you prove that it won't work for numbers 18 and above?

A Former Brilliant Member - 5 years, 9 months ago

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Apparently I read a book that said so P.S. I tested it P.S. obviously it works for 10 (considering the extra 0 at the end) so the remaining 8 are easy. But this is more than guess and check, this is testing how persistent you are.

Jian Yi Lee - 5 years, 9 months ago

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