A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Fool's problem of the day,
If \( n \) and \( m \) are natural numbers such that \( 1 + 2 + 3 + … + n = m^2 \), Find the sum of digits of the greatest such \( n \) , smaller than \( 10^3 \).
anonymous
 4 years ago
Fool's problem of the day, If \( n \) and \( m \) are natural numbers such that \( 1 + 2 + 3 + … + n = m^2 \), Find the sum of digits of the greatest such \( n \) , smaller than \( 10^3 \).

This Question is Closed

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1We're looking for a number \(m^2\) that's both triangular and perfect square. \(n<10^3 \implies m^2=\frac{n(n+1)}{2}<500500.\) The largest such \(m\) is \(41616\), that gives \(n(n+1)=2(41616) \implies n=288\). I cheated from here http://en.wikipedia.org/wiki/Square_triangular_number

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That's interesting MR.Math, however the challenge was a develop a solution that could be implemented without electronic aid ;)

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1I know, but I'm so lazy. Plus I know that a list of such numbers exist and there are not so many of them that are less than 500500. Steps to finding these numbers explicitly can be found in the link.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lol, Mr.Math this is a quantitative aptitude problem, think elementary ;)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.