The king is very angry at his two best mathematicians, so he decrees the following punishment:

The mathematicians will be imprisoned in towers at opposite ends of the kingdom. Each morning, a guard at each tower will flip a coin and show the result to his prisoner. Each prisoner must then guess the result of the coin flip at the other tower. If at least one of the two guesses is correct, they will live another day. But as soon as both guesses are incorrect, they will be executed.

The two mathematicians, as they were being ushered out the door of the castle, came up with a clever plan so that they will always be able to make at least one correct guess. What was their plan?

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