War of the Words timer 40s memory 1024MB

Finally, you are face to face with the leader of the alien robots! You have managed to distract it with its favorite word game, while your fellow Resistance members try to shut down the robots' power supply.

The game uses the robot language, which is made up of 10⁵ words: the set of all five-letter strings made up of uppercase English letters between A and J, inclusive. For example, AAAAA, FGHIJ, and BEIGE are among the valid words.

You know that these words have a rank order, with no ties, such that a higher-ranked word beats any lower-ranked word, with the one exception that the lowest-ranked word beats the highest-ranked word. Unfortunately, you do not know the rank order of the words in the robot language!

The game has the following rules:

• Turn 0: You start by naming a word W₀.
• Turn 1: The robot names a word W₁. If W₁ beats W₀, the robot scores a point.
• This continues; on turn i, the active player is you if i is even, or the robot if i is odd. The active player names a word W_i and scores a point if W_i beats W_i-1. (If the two words are the same, no point is scored.) The score is not announced — in particular, you will not know whether each of your words has scored a point!
• This continues for a total of 201 turns.
• Notice that you get the last turn (naming W₂₀₀), and that at the end of that turn, each player's score is between 0 and 100, inclusive.

Thanks to some great work by the Resistance's spies, you know the strategy that the robot will use for every turn of the game. It only cares about scoring 100 points, so on every turn, it will choose a word uniformly at random from all possible words that will score a point on that turn, and independently of all of its previous word choices. The robot knows the rank order of the language, so it has no trouble choosing words!

If you do not score at least N points, the robot will become bored and stop playing with you, so your plan (and the universe) will be doomed!