A triangle-shaped connection is made up of three 6 ohm resistors apiece. How strong is the bonding between the vertices?

Equivalent resistance $=6+6+\frac{1}{6}$ (since the first two are in series, and they are in parallel to the third in case of a triangular arrangement)
$\frac{1}{R}=12+\frac{1}{6}=\frac{(12+2)}{12}=\frac{14}{12}=\frac{7}{6}$
Thus, $R=\frac{1}{\frac{7}{6}}=\frac{6}{7}\Omega$ 
Therefore, the equivalent resistance is $\frac{6}{7}\Omega$ .