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

  • Thread starter Thread starter Tyrion101
  • Start date Start date
  • Tags Tags
    even Homework
AI Thread Summary
The discussion centers on the challenge of creating math problems that yield integer solutions, particularly in the context of right triangles and the Pythagorean theorem. The author expresses surprise at the prevalence of problems without decimals and questions why generating such problems is not more common. They highlight the simplicity of using known integer triangles, like the 3-4-5 triangle, and suggest that scaling these can easily produce new problems with integer solutions. The conversation also touches on the experience of students encountering decimal answers for the first time, noting that it can be a surprising realization for those new to the subject. Overall, the focus is on the ease of constructing integer-based problems versus the potential confusion for learners when faced with non-integer results.
Tyrion101
Messages
166
Reaction score
2
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?
 
Physics news on Phys.org
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!
 
Similar to the 2024 thread, here I start the 2025 thread. As always it is getting increasingly difficult to predict, so I will make a list based on other article predictions. You can also leave your prediction here. Here are the predictions of 2024 that did not make it: Peter Shor, David Deutsch and all the rest of the quantum computing community (various sources) Pablo Jarrillo Herrero, Allan McDonald and Rafi Bistritzer for magic angle in twisted graphene (various sources) Christoph...
Thread 'My experience as a hostage'
I believe it was the summer of 2001 that I made a trip to Peru for my work. I was a private contractor doing automation engineering and programming for various companies, including Frito Lay. Frito had purchased a snack food plant near Lima, Peru, and sent me down to oversee the upgrades to the systems and the startup. Peru was still suffering the ills of a recent civil war and I knew it was dicey, but the money was too good to pass up. It was a long trip to Lima; about 14 hours of airtime...
Back
Top