Find total resistance of this circuit

I want to find the total resistance between A and B. This is a HOTS mcq, which has the following options:

• A: 45$\Omega$


• B: 15$\Omega$


• C: 5$\Omega$


• D: 22.5$\Omega$

A book says that the answer is 5$\Omega$ as R1, R2 and R3 are parallel. But I cannot understand how can they be parallel? Our science teacher said that R1, R2 and R3 are in a series, so he said that total resistance R=45$\Omega$. The book that says that the answer is 5$\Omega$, does not have the method to find it out.

I tried that:

1. 
   

   All are in series :- 45$\Omega$

   
   


2. 
   

   15$\Omega$ is parallel with 15+15+15$\Omega$ and with one more 15$\Omega$, which would turn into : 45/7$\Omega$, which is not possible.

   
   


3. 
   

   R3 is parallel with R1 and R2, as well as in a series with R2. R1 is parallel with R2 and R3, as well as in a series with R2 and R3. But then I cannot determine the method to get the answer.

   
   

So I am confused between 5$\Omega$ and 45$\Omega$. I think as the book says, the answer must be 5$\Omega$, but what is the method?

Answer

the book is pretty correct as the circuit is like this:

^{simulate this circuit – Schematic created using CircuitLab} This circuit would be in series if there were no wires shorting the circuit and then net resistance would be 15 ohm.