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.