Problem 036

tOmcOlins · Post by **tOmcOlins** » Fri Jul 18, 2008 10:43 pm

is a single-digit number such as 3 considered to be a palindrome?

JohnMorris · Post by **JohnMorris** » Fri Jul 18, 2008 10:54 pm

fbarton · Post by **fbarton** » Wed May 06, 2009 1:28 pm

I also suggest re-wording the problem from

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

to

Find the sum of all natural numbers, less than one million, which are palindromic in base 10 and base 2.

Just for clarification's sake

Assato · Post by **Assato** » Thu May 07, 2009 4:03 am

Well, a palindromic number can't be negative, so in the end that wouldn't make much of a difference... unless you are trying to exclude FRACTIONAL palindromic numbers?

Anyway, the formal definition of Palindromic number from wikipedia (http://en.wikipedia.org/wiki/Palindromic_number) defines this concept only for natural numbers...

kvanvel · Post by **kvanvel** » Mon Mar 08, 2010 1:16 am

I am reasonably sure that there is an error in the solution to problem 36 http://projecteuler.net/index.php?secti ... lems&id=36.

Please note that according to the note about appending leading zeros,

811800 and 656000 are both palindromes. We can think of them as
00811800 and 000656000, respectively. Also the base 2 representations of these numbers are as follows;

11000110001100011000₂ for 811800 which we can pad with zeros to make 00011000110001100011000₂ which is a palindrome.

1010000000101000000₂ for 656000 which we can pad with zeros to make 0000001010000000101000000₂ which is also a palindrome.

These numbers, among others, are not listed in anyone's list of both base 10 and base 2 palindromes.

This is my first post, so I apologize if this should go someplace else. I tried not to disclose any hints on the "correct" answer. Thanks.

TripleM · Post by **TripleM** » Mon Mar 08, 2010 1:25 am

The note about leading zeroes says they are not allowed. You seem to have misread that and thought leading zeroes are allowed.

JeffsRealm · Post by **JeffsRealm** » Tue Mar 15, 2011 5:32 pm

Question about this problem,

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

I realize the example is 585 = 1001001001

So does this mean
Find the sum of all numbers, less than one million, which are palindromic in BOTH base 10 and base 2.

or

Find the sum of all numbers, less than one million, which are palindromic in base 10 then sum with the ones which are palindromic in base 2 as well.

I am guessing I will answer it myself soon enough but the wording was just odd if the number needs to be palindromic in both base 10 and base 2 to count. I am assuming this is the case and so will try it this way first.

JeffsRealm · Post by **JeffsRealm** » Tue Mar 15, 2011 5:43 pm

I guess I will answer my own question if someone comes looking

Yes the answer is

Find the sum of all numbers, less than one million, which are palindromic in BOTH base 10 and base 2.

So just like the 585 example is palindromic in both.

hooiberg · Post by **hooiberg** » Fri Jul 08, 2011 9:12 am

in most problems 'less than one million' is very clear. It is a bit ambiguous in this problem though, because 1000000 is a number both in base 10 and in base 2, however their numerical values are different.

Is it correct to assume that 'less than one million' refers to base 10?

jaap · Post by **jaap** » Fri Jul 08, 2011 9:22 am

hooiberg wrote:in most problems 'less than one million' is very clear. It is a bit ambiguous in this problem though, because 1000000 is a number both in base 10 and in base 2, however their numerical values are different.

Is it correct to assume that 'less than one million' refers to base 10?

That is why it says "one million" and not "1000000".

hooiberg · Post by **hooiberg** » Fri Jul 08, 2011 11:27 am

Okay, thank you for your fast reply.

Sintex · Post by **Sintex** » Tue Sep 06, 2011 5:37 pm

Could i ask i cant seem to find an issue with my code however Euler is saying its wrong,

Dose anyone know how many palindromic numbers in both bases there are under 1M.

Thanks

rayfil · Post by **rayfil** » Wed Sep 07, 2011 1:56 am

Dose anyone know how many palindromic numbers in both bases there are under 1M.

At the last count, 26639 persons have submitted the correct answer and must therefore know how many palindromic numbers in both bases there are under 1M. It's just a matter of counting them when adding them up.

Send me a PM with your count and I will answer you if it is correct or not.

bratbartka · Post by **bratbartka** » Tue Nov 01, 2011 1:57 pm

I wrote some algorithm which should works.. but it doesn't
I started from 11 till 999999
I suppose that from 1 to 10 there are 5 BOTH palindromic
1 - 1, 3 - 11, 5 -101, 7 -111, 9 - 1001
am I correct ?
I just wonder if there is some mistake in the start assumption or I should rather pay attention on algorithm ?
help, help, help

bratbartka · Post by **bratbartka** » Tue Nov 01, 2011 2:12 pm

OK
I war right
In my case I was counting these numbers instead of add them.
E.G.
below 11 there is 5 palindromic BOTH base
bu the sum is 1 + 3 + 5 + 7 + 9 = 25
and 25 should be the answer, not 5

springyboard · Post by **springyboard** » Mon Jan 30, 2023 5:45 pm

I joined the forum to post the exact same question but managed to find this topic in the search.

Perhaps we could discuss a better wording for the problem to clarify this.

bruce_love · Post by **bruce_love** » Mon Jan 30, 2023 9:46 pm

Please give your suggested wording.

Project Euler Forum

Problem 036

Problem 036

Re: problem 36 clarification

Re: Problem 036

Re: Problem 036

PROBLEM 36

Re: PROBLEM 36

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036

Re: Problem 036