# triangle problem

• Oct 2nd 2010, 01:01 AM
prasum
triangle problem
let t(n) denote the number of integer sided triangle with distinct sides chosen from(1,2,3...n) then t(20)-t(19) equals
• Oct 2nd 2010, 04:14 AM
Wilmer
Go here: The On-Line Encyclopedia of Integer Sequences™ (OEIS™)
Enter sequence number A002623
• Oct 2nd 2010, 05:22 AM
prasum
but how will i know this sequence
• Oct 2nd 2010, 05:56 AM
prasum
but they are integral sided triangles
• Oct 2nd 2010, 08:53 AM
Wilmer
I'm no longer sure I know what you're asking...or that you know what you're asking!

OK, answer this: using n=3, thus (1,2,3), how many integer sided triangles can you construct?
And list them, please: there's not many.
• Oct 2nd 2010, 09:13 AM
undefined
Quote:

Originally Posted by prasum
let t(n) denote the number of integer sided triangle with distinct sides chosen from(1,2,3...n) then t(20)-t(19) equals

I believe your question is very similar to this one

http://www.mathhelpforum.com/math-he...es-148807.html

• Oct 2nd 2010, 09:31 AM
Traveller
The answer to the OP's question is the number of triangles with integer sides and at least one side 20. The sum of the other two sides can vary from 21 to 40. So we can have 10 + 2* (11 + 12 + ... + 19 ) + 20 = 10 + 2*135 + 20 = 300.

EDIT : Sorry, overlooked the distinct sides part. The number of such isosceles triangles is 9 + 20 = 29. So the answer should be 300 - 29 = 271.
• Oct 2nd 2010, 09:47 AM
undefined
Quote:

Originally Posted by Traveller
The answer to the OP's question is the number of triangles with integer sides and at least one side 20. The sum of the other two sides can vary from 21 to 40. So we can have 10 + 2* (11 + 12 + ... + 19 ) + 20 = 10 + 2*135 + 20 = 300.

EDIT : Sorry, overlooked the distinct sides part. The number of such isosceles triangles is 9 + 20 = 29. So the answer should be 300 - 29 = 271.

Hmm I think your number is too high because for example wouldn't you get the 19 in parentheses by considering these triangles?

{20,1,38}
{20,2,36}
...
{20,19,19}

and

{20,1,39}
{20,2,37}
...
{20,19,20}

But a side length cannot be greater than 20.

I get 81 as explained in post #25 here, which I probably should have referenced before.
• Oct 2nd 2010, 10:05 AM
Traveller
My bad, thank you for the rectification. It is 81.
• Oct 2nd 2010, 10:40 AM
Wilmer
Quote:

Originally Posted by prasum
let t(n) denote the number of integer sided triangle with distinct sides chosen from(1,2,3...n) then t(20)-t(19) equals

Prasum, next time you post such an unclear problem, please
make sure it is understandable, plus supply a complete example;
this way, there will be less "running around"; thank you.