Project Euler Forum

I think the example with 10667 is wrong. After a couple of iterations it arrives to the palindrome 2326666232.
Although this isn't relevant as far as the problem is concerned, should be rectified

10667 + 76601 == 87268
87268 + 86278 == 173546
173546 + 645371 == 818917
818917 + 719818 == 1538735
1538735 + 5378351 == 6917086
6917086 + 6807196 == 13724282
13724282 + 28242731 == 41967013
41967013 + 31076914 == 73043927
73043927 + 72934037 == 145977964
145977964 + 469779541 == 615757505
615757505 + 505757516 == 1121515021
1121515021 + 1205151211 == 2326666232.

Paul.

ah, ignore me ; I'm being an idiot. the example was 10677

Hey guys,

This is obviously about Problem 55 (View Problem)

I solved it, I got all the Lychrel numbers below 10000. Mentioned in the question, 196 and 4994 are Lycherals. I got them which confirms my method is correct. But I don't know why my answer is not accepted as correct. I made sure millions of times. I don't know what I can say and what I can't say in order not to spoil. But I followed the 50 iterations rule mentioned in the question, I made sure that they occur exactly 50 times not more or less. I tried changing it to 49 iterations, I got a slightly different number. I tried it, it's also wrong. I'm pretty sure about my first answer. and don't know what can I be missing ?

If you can't think of anything to help me with, can you please explain EXACTLY what does "How many Lychrel numbers are there below ten-thousand?" in case I misunderstood it, which is not probable.

Thanks everyone

OOOPPPSSSSSS, that was the most unseen mistake I have ever did.

I used unsigned int thinking they'de be large enough, I WAS WRONG. had to use unsigned __int64 to avoid numbers being overlapped. DAMN IT. coding in C++ btw

I used unsigned int thinking they'de be large enough

It's just another example satisfying my usual signature.

I'm somewhat unclear on the parameters of the problem. Does the reverse of a number have to maintain the same length of digits? (e.g. if "1" is the reverse of "10", then 10+1 == 11, which is a palindrome.)

Seralt wrote:I'm somewhat unclear on the parameters of the problem. Does the reverse of a number have to maintain the same length of digits? (e.g. if "1" is the reverse of "10", then 10+1 == 11, which is a palindrome.)

Leading zeros are not allowed in this case. In your example, you're really doing 01+10 = 11. Hence, yes, the reverse of a number will have the same number of digits.

That help?

elendiastarman wrote: Leading zeros are not allowed in this case.

Please point to a PE problem that does allow leading zeroes... I was under the assumption that leading zeroes are disallowed for every single one of them (so far, this assumption hasn't been falsified)

Lord_Farin wrote:

elendiastarman wrote: Leading zeros are not allowed in this case.

Please point to a PE problem that does allow leading zeroes... I was under the assumption that leading zeroes are disallowed for every single one of them (so far, this assumption hasn't been falsified)

Hmm...I seem to remember that there was just one problem that did...but I may be wrong. No big deal.

Running into some issues on this one. My code definitely generates palindromes and only increments the answer if one is found. I think I'm missing some exclusion rules though. I am excluding numbers with leading 0s. I.E. 10 + 01. I just skip 10. So basically all numbers that are a multiple of 10 gets skipped. Beyond that it looks like the vast majority of numbers will add up to a palindrome before hitting 50 iterations. Is there a lower bound? Should I not allow numbers like 1, 2, etc? They will create a palindrome before 50 iterations as well. What other exclusions might I be missing?

Reading comprehension failure on my part. Read on wiki that Lychrel numbers are numbers that CAN'T be turned into palindromes. I read the description 10 times and kept thinking it meant Lychrels are numbers that can turn into palindromes. Leaving my silliness to hopefully be a warning to others.

I think the wording should be changed to "How many probable Lychrel numbers are there below ten-thousand?"
If a number satisfies the conditions presented int the question then the number is a probable Lychrel number.
None are actually known to exist.

When I output all the Lychrel Numbers less than 10000, numbers such as 89, 177 are displayed. I manually checked and found that at least till 10 iterations they don't yield a palindrome. Are they Lychrel numbers?
And did anyone else face this problem?

harishkrishnapsbb wrote:... at least till 10 iterations they don't yield a palindrome.

The problem states that you should try 50 iterations, and that if that still doesn't give a palindrome then you may assume it is a Lychrel number. The numbers 89 and 177 do produce palindromes within 50 iterations (24 and 15 iterations respectively).

Are 2,4,6 and 8 considered palindromes?

Yes, they read the same back to front to me.

Just thought I'd post a few tips, as I got some confused and misleading ideas from reading previous posts. Also in case you think your algorithm is correct but still not getting the right answer, here are few reasons I had to fumble through.

1) Leading zeroes are not candidates for discarding a number if they occur from the flip process. For example, if 280 must be tested as 280 + 82 = 362 (thanks to rayfil for pointing out a big oops ), is a valid first step. There are in fact a few Lychrel numbers that are multiples of 10.

2) Initially Palindromic Numbers Can be Lychrel Hehe I know this is stated in the problems but I overlooked it.

3) Data types, Data Types, Data Types!! I ran into a few overflow problems even with 64bit variables. The numbers get suprisingly big for additions.

For example, if 280 must be tested as 280 + 28 = 308, is a valid first step

WRONG.

280 + 082 = 362 would be a valid first step!

Do you have to reverse the number and add both the original and reversed number at least once before you can call the number palindromic if the initial number is palindromic?

Did you see this line of the problem, which makes the answer very clear:

Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.