Logic puzzle: there are three machines — one always pours coffee, one always pours tea, and the third pours randomly. The labels are all mixed up. How to determine which is which with the minimum number of coins?

To determine which vending machine is which, one coin and one test are enough:

1. Choose a vending machine with a "random" sign (it definitely does not match the contents, as all signs are mixed up).
2. Insert a coin and see what it dispenses — coffee or tea.

Since this vending machine cannot be random (its sign is incorrect), it either always dispenses coffee or always tea. Thus, we can be sure of the drink it provides.

3. Now, knowing the drink of this vending machine, we can determine the others:
   • The vending machine with a sign that matches the drink we just identified cannot be that drink (since signs are mixed up), so it is the random one.
   • The remaining vending machine is the one that dispenses the other drink.

In total, one test with one coin is enough.