Problem 125

[pills]

Hello all,

I'm stuck on problem 125. Although the algorithm seems simple and the code I wrote works for the example, I'm stuck with the "Sorry..." page when I try it for 10^8.
I've rewritten the code 3 times and always come up with the same answer, which leads me to believe I missed something in the problem itself.
Here are the answers (sum and number of palindromes) I get for 10^3, 10^4, ... ,10^8 :

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4164 11
20268 17
667526 30
15447478 60
313698021 112
snip

Any help or pointers are appreciated... I'm sure I'll have a "D'oh" moment when I figure out the answer, but I've been thinking about this problem so much that I just can't see what I'm doing wrong

Note : I didn't want to post my code in case it spoiled the problem for someone else, but if it's needed you can PM me.

TIA !

pills

[hk]

You should check for any duplicates.
(BTW i snipped away your answer for 10^8)

[pills]

And here it is... D'OH !

Many thanks hk !

[Sunhill]

Similar problem here. I've reworked my programme a few times. Struggled with the number of consecutive squares part for a little while, then had a moment of enlightening. The 11 palindromes mentioned in the example are up with no problems. But for 10^8 I got the "Sorry" page too. Taking advice already offered here, I've verified that there are no duplicates.

Here are my results so far:

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Upper limit 10^3, 11 palindromes, Sum to 4164
Upper limit 10^4, 16 palindromes, Sum to 15934
Upper limit 10^5, 22 palindromes, Sum to 312690
Upper limit 10^6, 29 palindromes, Sum to 3648319
Upper limit 10^7, 34 palindromes, Sum to 29636222
Upper limit 10^9, 40 palindromes, Sum to 988022429

Any advice welcome.

[stijn263]

You should've found (and removed) duplicates..

[daniel.is.fischer]

Your numbers are way off.
I could take a look at the code and see if there's a legitimate way to nudge you in the right direction.

[Sunhill]

That's shattering, yet not unexpected news.

I'll slog away myself for the time being, but may later take you up on your kind offer.

[Sunhill]

Cracked it.

Of course, I spent most of the morning looking at the minute details of all the complicated calculations and could find no error.

Then I discovered that I had set the maximum starting integer as 31, since 32²>1000. Smart move to get the result given in the example, but not much help when you want to go up to 10⁸.

Thanks for the help.

[DDgeva]

I'm trying to solve Problem 125 and I'm getting an incorrect answer.
It seems pretty simple and my algorithm appears to be correct. I even get correct output for the given example.

Can anyone please confirm any of these values:
For all numbers less than 10^5, the sum of the palindromic square sums is 667526.
For numbers less than 10^7, the sum is 313698021.
For numbers less than 10^10, the sum is 593978406425.

Is my program correct / close in any of these values?

[harryh]

@ DDgeva :

Please do not start a new topic, if one already exists for the problem you are trying to solve!

As you can see, your question was (mostly) already answered before...

[in3xes]

Seems everyone is getting correct answers for 10^3, But I am getting wrong answer, I have feeling that problem may be wrong, but all 3000 people can't make the same mistake to get the correct answer. So, I should be wrong, please tell where I have gone wrong

for < 10 ^3
55 [1, 2, 3, 4, 5]
505 [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
818 [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
77 [4, 5, 6]
636 [4, 5, 6, 7, 8, 9, 10, 11, 12]
595 [6, 7, 8, 9, 10, 11, 12]
181 [9, 10]
121 [11]
434 [11, 12, 13]
313 [12, 13]
545 [16, 17]
484 [22]
676 [26]
total = 5440

Everything seems to correct, I don't I can't figure out whether question is wrong or I am wrong...Help!!

[harryh]

Well, Problem 125 (View Problem) states :

Note that 1 = 0² + 1² has not been included as this problem is concerned with the squares of positive integers.

For the same reason, your values 121, 484 and 676 are not acceptable (they are not sums of squares of positive integers).
That leaves you with ten acceptable values (instead of eleven) and their sum is slightly less than that stated in the problem.
The value you've missed must be obvious now. Right ?

[in3xes]

Thanks, that solved it

[Junglemath]

It didn't take too long to figure out that the palindromes that are themselves squares are not meant to be included in the sum, but you really should include a note mentioning this explicitly, or at least change the wording of the problem. A sum with a single term is still a sum. Unnecessarily sloppy wording.