Another gem posted by Konstantin Knop on Facebook.
Puzzle. The Vicious Dragon captured two princesses, Evangelina and Oddetta, and placed them in different towers in his castle. Then the Vicious Dragon flipped a fair coin an infinite number of times. He informed Evangelina of all the results of the even tosses and Oddetta of all the results of the odd tosses. Next, the Dragon asks each princess to name the number of any toss whose result is unknown to her. In other words, Evangelina must name an odd number, and Oddetta must name an even number.
If the tosses named by Evangelina and Oddetta are the same (both are tails or both are heads), the Vicious Dragon gives each princess a cake and a pink plush bunny and sets them free. But if the results differ, the Vicious Dragon devours Evangelina and Oddetta with cranberry jam. The Dragon loves princesses and cranberry jam!
The princesses know the Vicious Dragon’s habits and could have agreed on strategies in advance. What are the chances of the princesses escaping if Oddetta names a number first, and Evangelina names her number, knowing which number Oddetta chose?