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Jane StreetInternInternQuestion #499

Implement the game Tetris in 30 minutes.

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Design a real-time system to process millions of trades per second. How would you ensure low latency, fault tolerance, and exactly-once processing?If I roll two dice, what is the expected value of the product of the two faces?Suppose we play a game with a die where we roll and sum our rolls. We can stop at any time, and the sum is our score. However, if our sum is ever a multiple of 10, our score becomes zero and our game is over. What strategy will yield the greatest expected score? What about if the target multiple is a value other than 10?What is the optimal strategy for winning in rock-paper-scissors if your opponent can only choose between rock and paper?In n coin tosses, what is the probability that the number of heads is even? Prove your result rigorously.

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