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Solving IMO 1989 #6 using Probability and Expectation

A Dicey Problem

Problem: Waldo rolls one standard (fair) 6-sided die repeatedly, keeping a running total of what he rolls. To three decimal places, what's the probability that he eventually reaches a total of exactly 1,000,000?

Hint: If you use your intuition the answer is a single division.

Bonus: Rigorously prove that what you did is correct.


  1. HI Chris , so whats the answer to this ? i dont think i was able to get near anything

  2. Hi Mohit, it's 1/3.5, which is just 1/(expected value of a single roll). I have some more details in another blog entry:

    A Dicey Problem: Solution


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