## The Vicious Dragon

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?

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1. #### SI:

100% probably of escape if Oddeta can convert the location of one H and one T to Evengelica. For example, Oddeta picks 2n+2 such that 2n+1 is H and 2n+3 is T.

2. #### Elliot:

100%

The ideal strategy (to expand on SI’s comment) is one where the choice conveys the position of a head and a tail coin flip.

For example, if they agreed ahead of time, that the first one to pick would pick a number where the flip before it was heads and the one after was tails.

So, if Oddetta picks 4, and Evangelina knows this, she also knows that flip 3 is heads and flip 5 is tails. She then selects between them based on what the result of flip 4 was (which she knows)