In the statement of this problem, the sentence "Define T(n) to be the sum of the perimeters of all non-congruent integer-sided triangles whose minimum bounding square has integer side length not exceeding n." is confusing to me. What does non-congruent imply here? If n = 10, do we sum the 3-4-5 triangle, or its inflated 6-8-10 cousin? Do we sum only the smallest triangles, or the largest, among those that are congruent?
(in the example, ignore for now that the 3-4-5 triangle doesn't have an integer-sided minimum bounding square)
Problem 998
Forum rules
As your posts will be visible to the general public you are requested to be thoughtful in not posting anything that might explicitly give away how to solve a particular problem.
This forum is NOT meant to discuss solution methods for a problem.
See also the topics:
Don't post any spoilers
Comments, questions and clarifications about PE problems.
As your posts will be visible to the general public you are requested to be thoughtful in not posting anything that might explicitly give away how to solve a particular problem.
This forum is NOT meant to discuss solution methods for a problem.
In particular don't post any code fragments or results.
Don't start begging others to give partial answers to problems
Don't ask for hints how to solve a problem
Don't start a new topic for a problem if there already exists one
Don't start begging others to give partial answers to problems
Don't ask for hints how to solve a problem
Don't start a new topic for a problem if there already exists one
See also the topics:
Don't post any spoilers
Comments, questions and clarifications about PE problems.
-
mdean
- Posts: 206
- Joined: Tue Aug 02, 2011 2:05 am
Re: Problem 998
The wording does sound a little strange. My interpretation would be to not treat (10,13,13) and (13,13,10) as 2 separate triangles.
-
heteroing
- Posts: 74
- Joined: Thu Sep 10, 2020 10:23 am
- Contact:
Re: Problem 998
Congruent triangles have the same size. I think you're thinking of similar triangles instead.aaeeoo wrote: Sat May 23, 2026 8:17 pm If n = 10, do we sum the 3-4-5 triangle, or its inflated 6-8-10 cousin? Do we sum only the smallest triangles, or the largest, among those that are congruent?
