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Random arcs

Choose, at random, three points on the circle x^2 + Y^2 = 1. Interpret them as cuts that
divide the circle into three arcs. Compute the expected length of the ...


Hitting time of brownian motion

Suppose a brownian motion starts at 0, what is the probability that it hits point x before time T?


Traveling Ants

(1) There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner. What is the probability that they do not collide?

(2)There are ...


Three wise men

Three wise men are locked in three rooms. Each day there there is, or there
is no light in each room.
During a certain finite initial period there is no ...

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The largest homogeneous rectangles in a binary matrix

Given a binary matrix of size m-by-n, design an efficient algorithm to find the largest homogeneous rectangles inside this binary matrix.