Problem 141

axelbrz · Post by **axelbrz** » Mon Oct 27, 2008 5:03 am

Hi! I'm trying to resolve the problem 141.

It says that the sum of all progressive perfect squares below one hundred thousand is 124657, but I'm not getting that sum, I can't get more numbers than these: 9, 10404 (<-- both on the problem) and XXXXX.

Can someone give me another progressive perfect square number below 100,000 with d, q and r numbers?

Thanks!

Axel.

daniel.is.fischer · Post by **daniel.is.fischer** » Mon Oct 27, 2008 5:23 am

There's one more than you found. You can determine the square, d, q and r from that.

axelbrz · Post by **axelbrz** » Mon Oct 27, 2008 5:38 am

Yeah, I've found it, I were to delete my post :)

But you've answered, so thanks!

estanford · Post by **estanford** » Fri Nov 27, 2009 12:27 pm

I just made a post in the solution forum for this problem that I think Euler (or anyone else responsible for curating the problem sets) should read.

hk · Post by hk » Fri Nov 27, 2009 1:58 pm

Post read and commented upon.

Lord_Farin · Post by **Lord_Farin** » Thu Sep 09, 2010 12:35 pm

After debugging my code for hours, I verified the perfect squares I found are progressive, that there are no overflow problems, and that my bounds are exact. However, the answer my code returns is wrong. I will be not as naive as to state the answer in the database is wrong, but I seriously am out of debugging ideas now. Moreover, since my algo returns correct squares, I am convinced it is correct.

Is there anybody willing to go through my code to see if there is something I overlooked?

TripleM · Post by **TripleM** » Fri Sep 10, 2010 2:40 am

Sure.

maomaoloverose · Post by **maomaoloverose** » Thu Mar 10, 2011 8:58 am

I have the same trouble. Maybe, i got a wrong formula.

Can someone give me another progressive perfect square number below 100,000(I got only three numbers: 9, 10404 and 1xxxx

).

GenePeer · Post by **GenePeer** » Thu Mar 10, 2011 1:57 pm

The problem statement gives their sum, and you have three already. There are four; you can deduce the fourth from that.

maomaoloverose · Post by **maomaoloverose** » Fri Mar 11, 2011 7:44 am

Now, i got ten numbers, but it's still wrong. I got two formula, i can't post them here.

so, can someone check my algorithm?

GenePeer · Post by **GenePeer** » Fri Mar 11, 2011 11:01 am

There are a lot more than just ten numbers. You are probably making generalisations just from observing patterns, which you can not absolutely justify. That would explain why you are missing numbers. Try and think it through again. For n to be a square, what forms must q,d, & r take? What is the size of the search-space?

oleglyamin · Post by **oleglyamin** » Mon Oct 22, 2012 6:47 pm

I've run into some minor problem with my algorithm.
Help me debug it, please.

There is a progressive perfect square close to 10^5, but less than it.
Could you tell me common ratio of the geometric sequence corresponding to this number?

Thanks.

UPDATE: Don't bother - I found it.

jake223 · Post by **jake223** » Sat Dec 01, 2012 7:24 pm

I get thirteen possible values for n, which add up to a number between five hundred million and one billion that ends in 37. My answer is wrong, but I get the right answer for the 10000 case. Am I way under, or is there something I may be doing wrong?

thundre · Post by **thundre** » Sat Dec 01, 2012 11:50 pm

jake223 wrote:I get thirteen possible values for n, which add up to a number between five hundred million and one billion that ends in 37. My answer is wrong, but I get the right answer for the 10000 case. Am I way under, or is there something I may be doing wrong?

That would be the right answer if the upper limit were one billion.
But the upper limit in this problem is one trillion (10¹²).

Erf_Erf · Post by **Erf_Erf** » Wed Jan 29, 2014 6:57 pm

I get the correct answer for 10^5, but not for 10^12. I guess it could have something to do with low integer precision. Are the following values correct?

10^6: 700738
10^8: 171436696
10^10: 23261047907

nicolas.patrois · Post by **nicolas.patrois** » Wed Jan 29, 2014 8:39 pm

Erf_Erf wrote: 10^6: 700738
10^8: 171436696
10^10: 23261047907

Yes.
Yes.
No.

fabianlischka · Post by **fabianlischka** » Mon Mar 31, 2014 11:42 am

[deleted]

hk · Post by hk » Mon Mar 31, 2014 1:16 pm

@Fabianlischka:
The caption of this forum reads:
"A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions."
So it's not a place to give hints nobody has been asking for.

fabianlischka · Post by **fabianlischka** » Sat Apr 05, 2014 9:48 am

@hk - noted!

larryleinweber · Post by **larryleinweber** » Sat Sep 20, 2014 8:04 pm

The title of problem 141 is "Investigating progressive numbers, n, which are also square" but probably should be "Investigating progressive numbers that are perfect squares." The symbol "n" is irrelevant to the title. The word "which" implies that the quality of being square is incidental to the problem. The world "also" would make more sense if the title with "Investigating numbers that are progressive and also square."

The word "which" is used in many other problems where "that" would be more accurate.

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