3 resistors problem

[Aghanim]

Everyone that knows basic parallel circuit know this equation: 1/R_total= 1/R₁ + 1/R₂ ........ + 1/R_n (I'm sorry if this looks ugly, I don't know how to do proper fractions here)

So, today my class is asked to research about science stuffs and to present it in front of my class. I was assigned to this topic and the teacher asked us to make 2 questions. Then, using 4,12,18 ohm as the value of the resistors, I go up front and present the question to my class. Unfortunately, the number is not in whole number (we call that number ugly, as we are not allowed to use calculators in the school exams and national exams).

So, here is my question/challenge for this KSP forum:

Find the value of R₁, R₂, R₃ such as:

1. All of them is in integers, including each of those resistance values and the final R_total value

2. The values must not be same

Post the results below!

Numbers that passed this criterion:

- 2,3,6 by PUNiSH3R

Edited March 12, 2014 by Aghanim

[PUNiSH3R]

R₁ = R₂ = R₃ = 3 (see below) comes to mind...

Edited March 12, 2014 by PUNiSH3R

[Aghanim]

Ohh I forgot to put that in, edited

Edit: All resistance at 1? Nice attempt to loophole the challenge, but no, it doesn't fit the first criteria. Proof:

1/1 + 1/1+ 1/1 = 3/1

To get final R_total value, you need to flip the fraction, so it becomes this: 1/3

The result is not integer, so it fails the first criteria

Edited March 12, 2014 by Aghanim

[PUNiSH3R]

Alright, R₁=2, R₂=3, R₃=6

[Padishar]

How about 2, 3 and 6 ohms?

Edit: Doh!

[Aghanim]

Alright it works

[PUNiSH3R]

To get final R_total value, you need to flip the fraction, so it becomes this: 1/3

The result is not integer, so it fails the first criteria

Sorry, it's late/early here, I meant R_n = 3, but that would have failed your "no repeated values" rule.

[Z-Man]

R₁=2, R₂=3, R₁=6, R_total=1.

<rant about it being perfectly possible to calculate using fractions without a calculator, and pointing out that the intermediate values you come across will be fractions no matter what>

<rant 2 about ninjas>

[Aghanim]

Ohh right..... I never think about that

You don't need to convert the final fraction into decimal, you could directly multiply it by current/divide voltage using it....