HSC Stuff > HSC Mathematics Extension 2

Maths Problem

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kamil9876:
Yeah in that case, there is only one substring "10000..00" with k zeroes. And that is precisely the one comming from that number . This is because a number cannot start with 0, yet it can't have more than k+1 digits. So the only way our number can be a palindrome is if the "100..00" substring is in the middle, but this gives a contradiction since walking a little bit to the left we get a lot of 9's, which are not found if you go a little bit to the right.

edit: exactly what brighstky said.

kamil9876:
I guess this approach works for bases >2  (since we are essentially arguing with three different digits, 0,1,9 )

How about for base 2? Of course if you start from 0 then it works in base 2 with n=2 i.e  0110   But what if in base 2 you start from 1?

Planck's constant:
This is problem 17 from the 22nd All Russian Mathematical Olympiad 1996.
I am not sure if there is a solution available anywhere

kamil9876:

--- Quote ---I am not sure if there is a solution available anywhere
--- End quote ---

Of course it is, right in this thread. Unless you are talking about the base 2 case?

Nagisa:

--- Quote from: kamil9876 on December 15, 2012, 11:24:10 pm ---Of course it is, right in this thread. Unless you are talking about the base 2 case?

--- End quote ---

haha

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