Problem 52659. Easy Sequences 15: Pythagorean Area with maximum Hypotenuse

Created by Ramon Villamangca

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<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 204px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">A pythagorean triangle is defined as a right triangle with all three sides having integer lengths. Examples of pythogorean triangles are [3 4 5], [6 8 10] and [5 12 13].</span></span></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For a given a limit 'n', 2 vectors are produced: 'A' and 'H', 'A' contains all unique areas of pythagorean triangles, less than or equal to 'n', while 'H' contains the largest possible hypotenuse for  each area in 'A'. </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Write a function with 2 outputs , 'a' and 'h', which are sums of the elements of 'A' and 'H', respectively.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">For example for n = 100, the produced vectors are:  A = [6; 24; 30; 54; 60; 84; 96]  and B = [5;10; 13; 15; 17; 25; 20].</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Therefore, the output shall be: [a h] = [354 105].</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">NOTE: Please check this link for reference: </span></span><a target='_blank' href = "https://oeis.org/A009112"><span style=""><span style="">https://oeis.org/A009112</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">.</span></span></div></div></div>

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18 Solutions
7 Solvers

Last Solution submitted on Jan 01, 2023

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David Hill on 9 Sep 2021

From the first test problem, you are missing the triple (9,12,15).
A should be [6; 24; 30; 54; 60; 84; 96] and
B should be [5;10; 13; 15; 17; 25; 20].

Ramon Villamangca on 9 Sep 2021

Hi David,
Should be OK now. Thanks.

David Hill on 9 Sep 2021

I believe my code should be correct. If you could look at my code, I believe you are missing some triples in other tests as well. I am getting larger values than the test suite and I verified that I don't have any duplicates and the areas are all <= to the input.

William on 9 Sep 2021

I am having the same experience as David, and have also been careful about duplication.

Ramon Villamangca on 9 Sep 2021

HI William/David,

I've checked your solutions and your answers are not the same. I've verified my answers with:

http://oeis.org/A009112/b009112.txt.

It seems to be OK.

Ramon Villamangca on 9 Sep 2021

I've added an OEIS link in the problem for reference.

David Hill on 9 Sep 2021

I was confused. I did all possible unique Pythagorean triples (some have the same area). You just want unique areas (and if the areas are the same, the largest hypothenuse). If you added, "unique" areas of all Pythagorean triangles, it would be clearer.

Ramon Villamangca on 9 Sep 2021

Hi David,

That's why we want to find "largest possible hypotenuse for each area". That doesn't make sense if we don't mean unique areas. Anyway, I changed the problem to make it even clearer. Thanks.

David Hill on 9 Sep 2021

I am now getting the correct A (verified based on OEIS) to 10000, but my max hypotheses must not be matching yours. I verified my code is selecting the maximum hypotheses for the same areas. I don't think I am doing anything wrong.

Ramon Villamangca on 9 Sep 2021

Hi David, consider your answer for 1,000. If a program is correct the area you will get there should match with OEIS also.

David Hill on 9 Sep 2021

I had a mistake in my code. Figured it out. Thanks.

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Problem 52659. Easy Sequences 15: Pythagorean Area with maximum Hypotenuse

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Problem 52659. Easy Sequences 15: Pythagorean Area with maximum Hypotenuse

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