Consider a unit cube. You start in a vertex A, the goal is to get to the opposite vertex B on a cube by making random jumps to one of the neighboring vertices. Assume probabilities to move to either direction to be equal. Compute the expected number of jumps to get to B.

Consider a unit cube. You start in a vertex A, the goal is to get to the opposite vertex B on a cube by making random jumps to one of the neighboring vertices. Assume probabilities to move to either direction to be equal. Compute the expected number of jumps to get to B.

### Heard on the Street

May. 5th, 2009 12:05 pm"However, this does leave one question unanswered: What is the most efficient way to find the lowest common multiple of a group of numbers?" Are they kidding me? We did it in the 5-6 grade.... I am not talking about a general computer problem of finding LCM for any number in the efficient way. The original problem is the following:

Find the smallest positive integer that leaves a remainder of 1 when it is divided by 2, a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, ....., a remainder of 9 when divided by 10.