A person has a 2 resistance coils. By using them singly, in series or in parallel, he obtains 2 ohm, 4 ohm, 12 ohm, and 16 ohm. What is the new resistance?
Given 4 resistances, and we need to sort out which one is which.
Assume that the resistances are non-zero.
We know that two resistances in parallel is always smaller than any of the two.
Similarly, two resistances in series is always greater than any of the two.
So the two single resistances are the middle values, namely 4Ω and 12Ω.
Let's check:
In series, total = 4+12=16Ω ok
In parallel, R=1/(1/4+1/12)=1/(4/12)=3Ω
does not equal the smallest of 2Ω.
Could you check if there is a typo in the question?