## 241. Math Puzzle $6 / 85$

An electronic door lock has a plug strip with 12 contact sockets as its "key". The lock opens when two specific contact sockets are connected.

How many combination possibilities must be tried in the worst case to find the correct "key"?
From the 12 contacts, two must be combined, which results in $12 \cdot 11=132$ possibilities. All combinations are counted twice due to the different order of connection, but the order does not matter when short-circuiting.

Thus, there are $x=\frac{132}{2}=66$ combination possibilities, and therefore, in the worst case, 66 attempts.