Little Red Riding Hood and Little Blue Riding Joe

Transcription

1 META Little Red Riding Hood and Little Blue Riding Joe Author: Keywords: Difficulty: Comments: Did you miss me? lush, FU 42 None Statement One fine morning Little Red, as usual, was riding Hood. In the lush green forest full of bright roses and a crimson moon above she spotted Little Blue, who was riding his grumpy horse, Joe. Here is a picture of the surroundings as seen by Red

2 And here is a picture of a lonely dog. Soon after spotting Little Blue, she spotted a large board behind him. That large board had a nice little number written on it. Here is the board: As you can probably see, the board is large, but not that large. It can only hold numbers three digits long. An old man once told me, Old is Gold. That day, I sold the old man and earned a lot of money. He sold for a whopping hundred dollars per gram.

3 After this, blue also turned around and amazingly, there was a exactly similar board behind Red with the same properties. However, there was a different number written in that board. Anyway, getting back to the point. By the time Red had finished admiring the large board, she noticed that Blue was nowhere to be seen. However, since this is perfectly normal, Hood could spot Joe and galloped towards him at exactly three hundred and thirty seven hours per minute. By the way, here is my hippo. Say Hi. As soon as Hood galloped towards Joe, Red saw a number written on Blue s hat. Here is the hat. Also, since Blue was actually an ancestor of Elizabeth, this old hat in question was worn by King Elizabeth the tenth. And again, due to quantum entanglement[ the definition is as follows Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the

4 quantum state of each particle cannot be described independently instead, a quantum state may be given for the system as a whole ], Blue also saw a number written on Reds hat, which again had the exact same properties as Blues hat, though the number was different. At this point Talian Dutt raises her hand, and complains that she cannot handle these many numbers. This hat is an interesting masterpiece in itself, it has a nice property that whenever we write a number on the hat, the hat automatically only shows its remainder with one thousand adding one. For example if you wrote 1001 on the hat, the hat would show 2. If you wrote 0 on the hat, it would show 1. After this, both Red and Blue reach into the world of inverses. The world is very beautiful. Every matrix that you write in this world is actually the inverse of itself.

5 Henceforth both Red and Blue go to their respective homes

6 However, before red goes to sleep, she plays a game of darts. Here are the rules for a game of darts: Dart Board Measurements: Standard height from the floor to the bullseye on the dartboard is 5 feet 8 inches, while the oche (distance between the front of the board and the toeline) should measure 7 f eet 9.25inches. Basic Rules: In a game of 501 the object is for one player or a team to be the first to reach zero from starting total of 501. In simple terms, after three darts are thrown, the throwing player subtracts the total scored from his current total u ntil he reaches zero. In order to reach zero each player must finish by throwing a double i.e. if player one has 36 remaining he must hit double 18 to win, while if player two has 45 remaining he must hit single 5, double 20 to win - or a another combination of scores provided the final dart scores on a double. Some versions of the game require a double start whereby players must begin the game with a double as well as checking out on a double. The World Grand Prix uses the double in, double out rule. Games can be played to a Best of format whereby a player or team winning three legs in a Best of Five Leg competition wins the match. The World Matchplay and UK Open events are examples of tournament played on a Best of format with legs as the scoring format. Games on the PDC ProTour are held over the Best of 11 Legs. Other tournaments will be played in Set format, whereby players must win a set by winning the Best of Five legs, before claiming the match in the Best of Five Sets. The PDC World Championship and World Grand Prix are played using the Set format, with differing lengths of games at each tournament.

7 After playing many games of darts, Red realised that the probability with which she hits the center point is the number she saw on the board divided by the number she saw on the hat. Now, as you already know, due to quantum entanglement something is going to happen. The counterintuitive predictions of quantum mechanics about strongly correlated systems were first discussed by Albert Einstein in 1935, in a joint paper with Boris Podolsky and Nathan Rosen.[1] In this study, they formulated the EPR paradox (Einstein, Podolsky, Rosen paradox), a thought experiment that attempted to show that quantum mechanical theory was incomplete. They wrote: We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete. [1] However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. Following the EPR paper, Erwin Schrdinger wrote a letter (in German) to Einstein in which he used the word Verschrnkung (translated by himself as entanglement) to describe the correlations between two particles that interact and then separate, as in the EPR experiment. [21] He shortly thereafter published a seminal paper defining and discussing the notion, and terming it entanglement. In the paper he recognized the importance of the concept, and stated:[2] I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. Like Einstein, Schrdinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity.[22] Einstein later famously derided entanglement as spukhafte Fernwirkung [23] or spooky action at a distance.

8 Blue was also playing darts, and he also realised that the probability with which he hits the center point is the number he saw on the board divided by the number he saw on the hat. The next day, both red and blue qualify to participate in the World Darts championship. Here they compete with each other. Einstein is the judge of their match, and since he is Einstein, he wants to determine the probability with which Red will win the match. The first person who hits the center point wins the match. However, he has solved the problem around one billion times, and now wants you to solve it.

9 Input The first line contains the numbers seen by Red, separated by a space followed by the numbers seen by Blue, separated by a space Output Output the probability of Red winning the match The answer will be considered correct if the absolute or relative error doesn t exceed 10 6 Constraints Did you read the problem statement? Sample Input Sample Output