Find the equivalent resistance between two ends of the following circuit

Label the three resistors each as r/3 and the nodes:

Left terminal = A
Right terminal = D

Between them are three resistors with wires:

• top wire connects A to node after second resistor
• bottom wire connects node between first and second resistor to D

step 1: identify node equivalences

Because of wires:

A ≡ node after second resistor
node between first and second ≡ D

So the circuit collapses to just two nodes A and D.

step 2: check each resistor

Each of the three resistors (r/3) is connected between A and D.

So all three are in parallel.

step 3: equivalent resistance

$$R_{eq}=\frac{r/3}{3}=\frac{r}{9}$$