Brain Teasers
Brain Teasers Trivia Mentalrobics Games Community
Personal Links
Submit a Teaser
Your Favorites
Your Watchlist
Browse Teasers
All

Cryptography
Group
Language
Letter-Equations
Logic
Logic-Grid
Math
Mystery
Optical-Illusions
Other
Probability
Rebus
Riddle
Science
Series
Situation
Trick
Trivia

Random
Daily Teasers
Search Teasers

Advanced Search
Add to Google Add to del.icio.us

More ways to get Braingle...

Triangle Numbers

Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.

 

Puzzle ID:#14508
Fun:*** (2.73)
Difficulty:*** (2.89)
Category:Series
Submitted By:Smithy*en*!

 

 

 



Triangle numbers are formed by adding successive integers, i.e.

1 = 1+0,
3 = 1+2,
6 = 1+2+3,
10 = 1+2+3+4,
etc.

So the first few triangle numbers would be:

1,3,6,10,15,21,28, ...

Suppose somebody tells you a random integer. How can you quickly find out whether or not it is a triangle number?





What Next?

  
  

See another brain teaser just like this one...

Or, just get a random brain teaser

If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.

 



Comments

jimbo*au*
Sep 19, 2003

Cool teaser! Here is another way. Double it. find the square root (approx) and round up and down to consecutive integers. If they give the double, it is triangular. Example 15 doubled is 30. Since it lies between 25 and 36 is square root is about 5.5. Rounding up and down make 5 and 6. 5x6 = 30 Yes!
smithy*en*
Sep 19, 2003

Nice method jimbo! - but I think my one's a little less complicated...
Mr_R
Dec 13, 2003

I'm scratching my head as to why the given solution works? Good mind itch though. I had to look at the answer.
(user deleted)
Jan 18, 2005

I don't get it!
(user deleted)
Jan 18, 2005

I don't get it!
brianz**
May 12, 2005

Wait...

A triangular number is of the form (n^2+n)/2 where n is an integer.
4n^2+4n+1 is that times 8 and then plus one which can be factored out to be (2n+1)^2

The square root of that is 2n+1 and is an integer as long as n is an integer or half an integer. Now if n is something like 1.5, (n^2+n)/2 will not be an integer. Therefore, your method works.

Good one!
lessthanjake789*us*
Jun 02, 2005

is there any particular mathematical reasont hat works out, or is it just a rnadom quirk of mathematics that applies?
(also, once into bigger numbers, that method wont be so quick, trying to figure out perfect square and what not, but this is interestingly related to partial sum formula, because thats what triangle numbers are, sum of all integers from 1 to X. so for any number x, Sum = (x/2)*(2+(x-1)) for example, x=10, sum = 5*(2+9) = 55, t'works. dont bother trying to figure out the summation formula, I am telling you it works
fatjohn
Aug 05, 2005

Never heard it explained with the multiply it by 8, add 1 and take its square solution. Nice twist, and good teaser.



Back to Top
   



Users in Chat : AgathaPerch 

Online Now: 10 users and 738 guests

Copyright © 1999-2014 | Updates | FAQ | RSS | Widgets | Links | Green | Subscribe | Contact | Privacy | Conditions | Advertise

Custom Search





Sign In A Create a free account