Identifying the Odd Resistor: How Many Measurements Are Needed with an Ohmmeter?

[fshiznit]

You receive a box of 9 resistors. All the resistors except one have a value of 1 ohm. With only an ohmmeter, what is the minimum number of measurements needed to identify the odd resistor and find its resistance.

-I've tried going up from one resistor, but I'm not sure what I'm doing past 4 resistors :S..any help is much appreciated!

 

[Gokul43201]

-I've tried going up from one resistor, but I'm not sure what I'm doing past 4 resistors :S..any help is much appreciated!

What do you mean by "going up from one resistor"? Please be more explicit in your explanation.

 

[fshiznit]

so for let's say 3 resistors, you'll need two measurements because say you take an even one and an odd one and get a resistance of 2.1 ohm (that's one measurement) then you take one off to which is the odd one and its resistance (second measurement). but now I am thinking, wouldn't the minimum measurements, even for the 9 resistor one, be just two measurements, seeing that you get lucky and pick the odd one when testing the first two resistors? But then i guess the question'd be too easy :S

 

[Redbelly98]

As I interpret the question, assuming you are unlucky, what is the minimum number of measurements required?

A naive approach would be to measure them one-by-one and the odd one is the last resistor. However, you have to be a little clever here. Other than measuring one at a time, how else might you approach the problem?

 

[sberxasberxa]

would it make sense to put them in groups of 2 in parallel? (thus making 4 groups in series). Would that not only take a max. of 5 measurements depending on your luck?

 

[mplayer]

Hint: measure resistances across multiple elements at once and think about what that tells you. You cannot rely on luck to get the minimum number of measurements.

 

[Redbelly98]

FYI to everybody:

We really should let fshiznit try to solve the problem, and let him/her respond with questions, before giving further help.