Problem 009

ramchand · Post by **ramchand** » Thu Apr 20, 2006 8:59 pm

Regarding Problem 9 of the original Mathschallenge problems,
There exists exactly one Pythagorean triplet for which a + b + c = 1000
I fail to see the unique solution and doubt whether it exists.
Can anyone answer this query?
Thanks

quintic · Post by **quintic** » Thu Apr 20, 2006 9:26 pm

I don't want to give anything away, but I can say there is definitely a solution! And it is unique.

euler · Post by **euler** » Thu Apr 20, 2006 9:57 pm

Hi ramchand,

I've moved this to the "Programming Problems" section.

Like quintic said we are not able to give too much away, but I hope you've realised that the equation a + b + c = 1000 is not given in isolation; that equation certainly does not have unique solutions. But the problem states that a, b, and c are a Pythagorean triplet, which means that it is also true that a² + b² = c².

[edit]Edited to remove hint - after all we don't want to take away the fun in solving the problem![/edit]

wwtucker · Post by **wwtucker** » Fri Apr 21, 2006 8:28 am

Here's a way of explaning the problem without giving away and hints toward the solution.

We want positive integers: a,b,c such that a+b+c=1000 and a²+b²=c². It is clear by inspection that there are only a finite number of possibilities - the problem statement claims that there is only one set of a,b,c that works and (essentially) asks you to find it.

ramchand · Post by **ramchand** » Sun Apr 23, 2006 9:19 pm

Thanks.
Having the assurance that the solution exists, I solved it soon enough.

balex4o · Post by **balex4o** » Sun Jan 13, 2008 11:35 am

Hallo,
i've been trying to solve Problem 9 and i've found the answer, but it says that my answer is wrong

I've been looking in Internet for the answer and i've found the same answer [removed by moderator]. Is there a problem with the website, oder i think wrong

Code: Select all

[removed by moderator]

euler · Post by **euler** » Sun Jan 13, 2008 12:09 pm

Hi balex4o. I had to edit your post because you posted the correct answer and a program that would give the right answer.

Could you try submitting your answer again and let me know if the problem persists?

balex4o · Post by **balex4o** » Sun Jan 13, 2008 1:26 pm

Well, now is everything all right ! :=)

HazardTW · Post by **HazardTW** » Mon Nov 10, 2008 6:57 am

I was trying problem #9 but do not know how to enter my answer in the text input box, ie. should it be a=###, b=###, c=### ?

... or maybe ###+###+###=1000 ?

uws8505 · Post by **uws8505** » Mon Nov 10, 2008 7:19 am

As indicated in the problem, you should enter the product of the three numbers a*b*c.

badperson · Post by **badperson** » Sat Jan 24, 2009 8:26 pm

Hi,
In the pythagorean triplet problem, the example given for a^2 + b^2 = c^2

is 3^2(9) + 4^2(16) = 5^2(25)

so the answer is 25, which has a square root of 5.

the problem is supposed to end up with an answer of 1000, but 1000 doesn't have a perfect square (I mean a square root that is a whole number, maybe I'm using the wrong terminology there)

also, in the problem description, it says this:

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc

a + b + c implies three numbers whose sum equals 1000,

"find the product abc" implies a x b x c....

my program so far finds two incorrect solutions:

100(a) + 324(b) + 576(c) = 1000
total2 is: 424
10 x 10 = 100
10 x 10 = 100
18 x 18 = 324
18 x 18 = 324
24 x 24 = 576
24 x 24 = 576
are the roots 10, 18 and 24 a pythag triangle? false
36(a) + 64(b) + 900(c) = 1000
total2 is: 100
6 x 6 = 36
6 x 6 = 36
8 x 8 = 64
8 x 8 = 64
30 x 30 = 900
30 x 30 = 900
are the roots 6, 8 and 30 a pythag triangle? false

Can anyone point me in the right direction?
thanks!
bp

daniel.is.fischer · Post by **daniel.is.fischer** » Sat Jan 24, 2009 8:35 pm

It's not the squares that should sum up to 1000, but the lengths a, b and c themselves.
You have to find a, b and c with

a+b+c=1000,
a²+b² = c².

badperson · Post by **badperson** » Sat Jan 24, 2009 9:28 pm

gotcha...
reworked the program, and I thought I had it right, but it's not accepting my answer:

snip

I checked, and that is a pythag triplet... am I doing it wrong?

Tommy137 · Post by **Tommy137** » Sat Jan 24, 2009 9:48 pm

You must enter the product a*b*c.

And please edit your post and delete your solution.

badperson · Post by **badperson** » Sat Jan 24, 2009 10:10 pm

ok, got it, and so sorry about posting the solution, I won't do that in the future.
thanks,
bp

rayfil · Post by **rayfil** » Sun Jan 25, 2009 3:06 am

And there is a special forum for those kinds of questions relating to specific Project Euler problems. Its title is quite descriptive.

ProjectEuler Problems

Please use it in the future after making sure you read the first "sticky" post.

hk · Post by hk » Sun Jan 25, 2009 9:57 am

Can someone remember me to merge it with viewtopic.php?f=50&t=1204#p593
(Same problem was treated there)

DaRabman · Post by **DaRabman** » Tue Oct 13, 2009 11:12 pm

Hi there, I'm fairly sure that my answer to Problem 9 (View Problem) is correct, and wanted to clear up the policy on form. My answer has a decimal place, should it be rounded to an integer, and if not, how many significant figures?
Thanks,
Sam.

elendiastarman · Post by **elendiastarman** » Tue Oct 13, 2009 11:25 pm

a, b, and c should all be integers and as such the product should be an integer. Methinks you're allowing a decimal into one of the three...

craigcussler · Post by **craigcussler** » Thu Nov 11, 2010 11:47 am

hello, I'm trying to solve the 9th problem, so i created asimple python code:

but the answer seems to be incorrect! please can you help me to find what's wrong?

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