How long does it take to make homework that comes out even, when there

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Discussion Overview

The discussion revolves around the challenges of creating mathematical homework problems that yield integer solutions, particularly in the context of right triangles and the Pythagorean theorem. Participants explore the ease or difficulty of formulating such problems without decimals, reflecting on their experiences and observations in problem creation.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested, Homework-related

Main Points Raised

  • One participant expresses surprise at the prevalence of problems without decimals and questions how long it takes to find such problems.
  • Another participant argues that creating problems with integer solutions should not take any time at all, suggesting it is a straightforward task.
  • A participant discusses the ease of generating problems involving right triangles, specifically referencing the 3-4-5 triangle and its scalability, indicating that integer solutions can be derived easily.
  • One suggestion is to determine the desired answer first and then work backwards to create the problem, implying a strategic approach to problem formulation.
  • A participant reflects on the experience of students encountering decimal answers for the first time, noting that it can be surprising for those new to the subject.

Areas of Agreement / Disagreement

There is no consensus on the time required to create problems with integer solutions. Some participants believe it should be easy and quick, while others acknowledge the challenges faced by learners.

Contextual Notes

Participants do not specify the assumptions or constraints that might affect the problem creation process, nor do they address potential limitations in the types of problems discussed.

Tyrion101
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I'm starting to get to a point where the numbers are getting sometimes well beyond 3 digits in length and, I'm constantly amazed at the fact that there are usually no decimals anyplace in the actual problem, and I was wondering how long does it take to find questions that don't have decimals in the problem?
 
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I don't see why it should take any time at all. How hard can it be to make up problems that have integer solutions?
 
If the problem involves right triangles (utilizing the Pythagorean therem, c2 = a2 + b2) then it ends up pretty easy if the triangles are 3-4-5 triangles (52 = 32 + 42).

You can also scale the 3, 4 and 5 by any constant and it still works out. For example, let's multiply them all by 123.

c2 = 3692 + 4922.

Solve for c.
 
Last edited:
A good way is first decide what you want the answer to be, then work backwards to find the numbers in the question.
 
phinds said:
I don't see why it should take any time at all. How hard can it be to make up problems that have integer solutions?

Not very hard for those who can easily solve them forwards and back. But for someone first learning, it's an interesting observation. I wonder how many students are shocked the first time they get an answer that has a digits after the decimal, and realize it's a correct answer!
 

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