# Thread: triangle problem

1. ## 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

2. Go here: The On-Line Encyclopedia of Integer Sequences™ (OEIS™)
Enter sequence number A002623

3. but how will i know this sequence

4. but they are integral sided triangles

5. 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.

6. 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

Ignore my initial comments where I misinterpreted what was being asked.

7. 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.

8. 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.

9. My bad, thank you for the rectification. It is 81.

10. 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.