There is a unit cube with internal mirror faces. A ray is emitted into the cube from one vertex, reflects off four faces (without touching vertices or edges), and stops at the opposite vertex from which it started. What is the minimum possible distance the ray travels? The answer should be decimal format approximated to 4 digits of precision, i.e. format a.bcd as in 1.234.
The probability of rolling two dice. 6, 6 gets 100, 6, not 6 loses x, and other cases you redo the dice rolling. When should you play the game?
Nine fair coins are tossed, what is the probability of an odd number of heads landing?
How do you estimate square root of 5?
You have a path of length n. You flip a coin, if heads move one space and if tails move two spaces. You keep flipping until you reach the end. If P(i) is the probability of landing on space i, for what value of i is P(i) maximized?
You play a game with someone, the rule is to take turns to put a quarter on a round table ( can be any size, but must be of symmetrical shape). You are trying to cover the table up with quarters, you lose when there's no place for you to put down the quarter. Should you be the first person to play ?
Find the minimum of x^x
Run one iteration of bubble sort. What's the probability that the array is now sorted?
Maximizing Sharpe ratio related question
How many N in [100,400] s.t. N^N is perfect square
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